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Algorithms
Volume 15
Issue 3
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Algorithms, Volume 15, Issue 3 (March 2022) – 30 articles

Cover Story (view full-size image): Reinforcement learning (RL) with sparse rewards is still an open challenge. Classic methods rely on learning via extrinsic rewards, and in situations where these are sparse, the agent may not learn at all. Similarly, if the agent gets rewards that create suboptimal modes of the objective function, it will prematurely stop exploring. Recent methods add intrinsic rewards to encourage exploration, but they lead to a non-stationary target for the Q-function. In this paper, we present a novel approach that (1) plans exploration far into the future using a long-term visit count and (2) decouples exploration and exploitation by learning a separate function. We also propose new environments for benchmarking exploration in RL. Results show that our approach outperforms existing methods. View this paper
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19 pages, 1080 KiB  
Article
Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems
by Markus P. Rumpfkeil, Dean Bryson and Phil Beran
Algorithms 2022, 15(3), 101; https://doi.org/10.3390/a15030101 - 21 Mar 2022
Cited by 5 | Viewed by 3043
Abstract
In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating [...] Read more.
In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating a large number of designs for uncertainty quantification, optimization, or design space exploration. Analytical benchmark problems are used to show that accurate multi-fidelity surrogate models can be obtained at lower computational cost than high-fidelity models. The benchmarks include non-polynomial and polynomial functions of various input dimensions, lower dimensional heterogeneous non-polynomial functions, as well as a coupled spring-mass-system. Overall, multi-fidelity models are more accurate than high-fidelity ones for the same cost, especially when only a few high-fidelity training points are employed. Full-order PCEs tend to be a factor of two or so worse than SPCES in terms of overall accuracy. The combination of the two approaches into the SPCE-Kriging model leads to a more accurate and flexible method overall. Full article
(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)
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<p>MF kriging algorithm flowchart.</p> Full article ">Figure 2
<p>All four fidelity levels of Forrester function.</p> Full article ">Figure 3
<p>Rosenbrock function (from left to right, high-, medium-, and low-fidelity).</p> Full article ">Figure 4
<p>Shifted-rotated Rastrigin function (from left to right, high-, medium-, and low-fidelity).</p> Full article ">Figure 5
<p>Plot of one- (<b>left</b>) and two-dimensional (<b>right</b>) HF and LF ALOS functions with initial HF training points.</p> Full article ">Figure 6
<p>Springs connecting three masses.</p> Full article ">Figure 7
<p>Analytical solution for the spring-mass problem for <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mn>30</mn> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Numerical solution for <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the example problem for <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mn>6</mn> </mrow> </semantics></math> using <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math> labeled as high-fidelity (HF) and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math> labeled as low-fidelity (LF).</p> Full article ">Figure 9
<p><math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>=</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>≤</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>4</mn> </mrow> </semantics></math> with HF and LF results shown in red and blue, respectively.</p> Full article ">Figure 10
<p>Forrester function RMSE (from left to right, PCE and kriging).</p> Full article ">Figure 11
<p>PCE: Rosenbrock function RMSE (from left to right, two, five and ten dimensions). PCE and SPCE in dashed and solid lines, respectively.</p> Full article ">Figure 12
<p>Kriging: Rosenbrock function RMSE (from left to right, two, five and ten dimensions). Ordinary and SPCE-Kriging in dashed and solid lines, respectively.</p> Full article ">Figure 13
<p>PCE: Rastrigin function RMSE (from left to right, two, five and ten dimensions). PCE and SPCE in dashed and solid lines, respectively.</p> Full article ">Figure 14
<p>Kriging: Rastrigin function RMSE (from left to right, two, five and ten dimensions). Ordinary and SPCE-Kriging in dashed and solid lines, respectively.</p> Full article ">Figure 15
<p>PCE: ALOS function RMSE (from left to right, one, two and three dimensions). PCE and SPCE in dashed and solid lines, respectively.</p> Full article ">Figure 16
<p>Kriging: ALOS function RMSE (from left to right, one, two and three dimensions). Ordinary and SPCE-Kriging in dashed and solid lines, respectively.</p> Full article ">Figure 17
<p>Spring-mass system (only springs) RMSE (from left to right, PCE and Kriging).</p> Full article ">Figure 18
<p>Spring-Mass System RMSE (from left to right, PCE and Kriging).</p> Full article ">
21 pages, 498 KiB  
Article
Key Concepts, Weakness and Benchmark on Hash Table Data Structures
by Santiago Tapia-Fernández, Daniel García-García and Pablo García-Hernandez
Algorithms 2022, 15(3), 100; https://doi.org/10.3390/a15030100 - 21 Mar 2022
Cited by 4 | Viewed by 3967
Abstract
Most computer programs or applications need fast data structures. The performance of a data structure is necessarily influenced by the complexity of its common operations; thus, any data-structure that exhibits a theoretical complexity of amortized constant time in several of its main operations [...] Read more.
Most computer programs or applications need fast data structures. The performance of a data structure is necessarily influenced by the complexity of its common operations; thus, any data-structure that exhibits a theoretical complexity of amortized constant time in several of its main operations should draw a lot of attention. Such is the case of a family of data structures that is called hash tables. However, what is the real efficiency of these hash tables? That is an interesting question with no simple answer and there are some issues to be considered. Of course, there is not a unique hash table; in fact, there are several sub-groups of hash tables, and, even more, not all programming languages use the same variety of hash tables in their default hash table implementation, neither they have the same interface. Nevertheless, all hash tables do have a common issue: they have to solve hash collisions; that is a potential weakness and it also induces a classification of hash tables according to the strategy to solve collisions. In this paper, some key concepts about hash tables are exposed and some definitions about those key concepts are reviewed and clarified, especially in order to study the characteristics of the main strategies to implement hash tables and how they deal with hash collisions. Then, some benchmark cases are designed and presented to assess the performance of hash tables. The cases have been designed to be randomized, to be self-tested, to be representative of a real user cases, and to expose and analyze the impact of different factors over the performance across different hash tables and programming languages. Then, all cases have been programmed using C++, Java and Python and analyzed in terms of interfaces and efficiency (time and memory). The benchmark yields important results about the performance of these structures and its (lack of) relationship with complexity analysis. Full article
(This article belongs to the Special Issue Surveys in Algorithm Analysis and Complexity Theory)
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<p>Case A. C++ <tt>std::unordered_map</tt> lookup speeds (<math display="inline"> <semantics> <mrow> <mi>s</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> <mo>=</mo> <msup> <mn>2</mn> <mn>20</mn> </msup> </mrow> </semantics> </math>).</p> Full article ">Figure 2
<p>Case A. Java <tt>HashMap</tt> building speeds (<math display="inline"> <semantics> <mrow> <mi>s</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> <mo>=</mo> <msup> <mn>2</mn> <mn>20</mn> </msup> </mrow> </semantics> </math>).</p> Full article ">Figure 3
<p>Case A. Removal Speed in python <tt>dict</tt> (<math display="inline"> <semantics> <mrow> <mi>s</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> <mo>=</mo> <msup> <mn>2</mn> <mn>20</mn> </msup> </mrow> </semantics> </math>).</p> Full article ">Figure 4
<p>Case B. <tt>std::map</tt> lookup speeds.</p> Full article ">Figure 5
<p>Case B.<tt>std::unordered_map</tt> lookup speeds.</p> Full article ">Figure 6
<p>Case B. Array-adapter lookup speeds.</p> Full article ">Figure 7
<p>Case B. Lookup speeds (<math display="inline"> <semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>).</p> Full article ">Figure 8
<p>Case B. Lookup speeds (<math display="inline"> <semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>).</p> Full article ">Figure 9
<p>Case C. Insertion/Removal vs. Access Speed.</p> Full article ">Figure 10
<p>Case C. Insertion/Removal vs. Access Speed.</p> Full article ">Figure 11
<p>Case D. Building Speed in Java.</p> Full article ">Figure 12
<p>Case F. Lookup Speed in C++.</p> Full article ">Figure 13
<p>Case F. Memory Use.</p> Full article ">Figure 14
<p>Cases D and G. Memory Use.</p> Full article ">Figure 15
<p>Case E. Building Speed in C++.</p> Full article ">Figure 16
<p>Case E. Lookup Speed in C++.</p> Full article ">Figure 17
<p>Case E. Lookup Speeds.</p> Full article ">
16 pages, 4336 KiB  
Article
Design of Selective Laser Melting (SLM) Structures: Consideration of Different Material Properties in Multiple Surface Layers Resulting from the Manufacturing in a Topology Optimization
by Jan Holoch, Sven Lenhardt, Sven Revfi and Albert Albers
Algorithms 2022, 15(3), 99; https://doi.org/10.3390/a15030099 - 19 Mar 2022
Cited by 4 | Viewed by 3470
Abstract
Topology optimization offers a possibility to derive load-compliant structures. These structures tend to be complex, and conventional manufacturing offers only limited possibilities for their production. Additive manufacturing provides a remedy due to its high design freedom. However, this type of manufacturing can cause [...] Read more.
Topology optimization offers a possibility to derive load-compliant structures. These structures tend to be complex, and conventional manufacturing offers only limited possibilities for their production. Additive manufacturing provides a remedy due to its high design freedom. However, this type of manufacturing can cause areas of different material properties in the final part. For example, in selective laser melting, three areas of different porosity can occur depending on the process parameters, the geometry of the part and the print direction, resulting in a direct interrelation between manufacturing and design. In order to address this interrelation in design finding, this contribution presents an optimization method in which the three porous areas are identified and the associated material properties are considered iteratively in a topology optimization. For this purpose, the topology optimization is interrupted in each iteration. Afterwards, the three areas as well as the material properties are determined and transferred back to the topology optimization, whereby those properties are used for the calculation of the next iteration. By using the optimization method, a design with increased volume-specific stiffness compared to a design of a standard topology optimization can be created and will be used in the future as a basis for the extension by a global strength constraint to maintain the maximum permissible stress and the minimum wall thickness. Full article
(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)
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<p>Exemplary representation (cut through <span class="html-italic">x</span>–<span class="html-italic">y</span> plane) of the three porous areas (<b>left</b>) and CT scan to visualize the porosity distribution in one print layer (<b>right</b>) adapted from [<a href="#B17-algorithms-15-00099" class="html-bibr">17</a>].</p> Full article ">Figure 2
<p>Workflow of the developed optimization method.</p> Full article ">Figure 3
<p>Surface meshes of the interim result (<b>top</b>) as well as offset 1 (<b>center</b>) and offset 2 (<b>bottom</b>).</p> Full article ">Figure 4
<p>Surface meshes (<b>top</b>) as well as meshed areas including assigned material properties of the interim result (<b>bottom</b>).</p> Full article ">Figure 5
<p>Porous areas including assigned material properties of the interim result considering the print direction (<b>top</b>) and material properties transferred to the initial topology optimization mesh (<b>bottom</b>).</p> Full article ">Figure 6
<p>Three-point bending beam with dimensions, clamping and loading.</p> Full article ">Figure 7
<p>Result of the developed optimization method: overall design (<b>left</b>) and sectional view (<b>right</b>).</p> Full article ">Figure 8
<p>Result of the standard topology optimization: overall design (<b>left</b>) and sectional view (<b>right</b>).</p> Full article ">Figure 9
<p>Comparison of the optimization history of the standard topology optimization and the developed optimization method.</p> Full article ">Figure 10
<p>Resulting design of the developed optimization method including porous areas (<b>left</b>) and result of the static FE analysis (<b>right</b>).</p> Full article ">Figure 11
<p>Resulting design of the standard topology optimization including porous areas (<b>left</b>) and result of the static FE analysis (<b>right</b>).</p> Full article ">Figure 12
<p>Section in the layer plane through the design from the developed optimization method: front view (<b>top</b>) and plan view (<b>bottom</b>).</p> Full article ">
18 pages, 576 KiB  
Article
Evolutionary Optimization of Spiking Neural P Systems for Remaining Useful Life Prediction
by Leonardo Lucio Custode, Hyunho Mo, Andrea Ferigo and Giovanni Iacca
Algorithms 2022, 15(3), 98; https://doi.org/10.3390/a15030098 - 19 Mar 2022
Cited by 9 | Viewed by 4554
Abstract
Remaining useful life (RUL) prediction is a key enabler for predictive maintenance. In fact, the possibility of accurately and reliably predicting the RUL of a system, based on a record of its monitoring data, can allow users to schedule maintenance interventions before faults [...] Read more.
Remaining useful life (RUL) prediction is a key enabler for predictive maintenance. In fact, the possibility of accurately and reliably predicting the RUL of a system, based on a record of its monitoring data, can allow users to schedule maintenance interventions before faults occur. In the recent literature, several data-driven methods for RUL prediction have been proposed. However, most of them are based on traditional (connectivist) neural networks, such as convolutional neural networks, and alternative mechanisms have barely been explored. Here, we tackle the RUL prediction problem for the first time by using a membrane computing paradigm, namely that of Spiking Neural P (in short, SN P) systems. First, we show how SN P systems can be adapted to handle the RUL prediction problem. Then, we propose the use of a neuro-evolutionary algorithm to optimize the structure and parameters of the SN P systems. Our results on two datasets, namely the CMAPSS and new CMAPSS benchmarks from NASA, are fairly comparable with those obtained by much more complex deep networks, showing a reasonable compromise between performance and number of trainable parameters, which in turn correlates with memory consumption and computing time. Full article
(This article belongs to the Special Issue Algorithms in Decision Support Systems Vol. 2)
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<p>Flow chart of a data-driven RUL prediction task.</p> Full article ">Figure 2
<p>Illustration of the Symbolic Fourier Approximation process. <math display="inline"><semantics> <msub> <mi>X</mi> <mi>i</mi> </msub> </semantics></math> denotes a selected Fourier coefficient, and <math display="inline"><semantics> <msub> <mi>o</mi> <mi>i</mi> </msub> </semantics></math> represents each output symbol from the SFA.</p> Full article ">Figure 3
<p>Fitness across generations (mean ± std. dev. across 10 independent runs) for SNPS (5) on CMAPSS (FD001).</p> Full article ">Figure 4
<p>Fitness across generations (mean ± std. dev. across 10 independent runs) for SNPS (4) on N-CMAPSS (DS02).</p> Full article ">Figure 5
<p>Best SN P system evolved for the RUL prediction task on CMAPSS (FD001).</p> Full article ">Figure 6
<p>Trade-off between test RMSE and number of trainable parameters for the methods considered in the experimentation on CMAPSS (FD001).</p> Full article ">Figure 7
<p>Trade-off between test RMSE and number of trainable parameters for the methods considered in the experimentation on N-CMAPSS (DS02).</p> Full article ">Figure 8
<p>Best SN P system evolved for the RUL prediction task on N-CMAPSS (DS02).</p> Full article ">
3 pages, 166 KiB  
Editorial
Editorial for the Special Issue on “Machine Learning in Healthcare and Biomedical Application”
by Alessia Sarica
Algorithms 2022, 15(3), 97; https://doi.org/10.3390/a15030097 - 19 Mar 2022
Cited by 6 | Viewed by 2549
Abstract
In the last decade, Machine Learning (ML) has indisputably had a pervasive application in healthcare and biomedical applications [...] Full article
30 pages, 1418 KiB  
Article
A Dynamic Distributed Deterministic Load-Balancer for Decentralized Hierarchical Infrastructures
by Spyros Sioutas, Efrosini Sourla, Kostas Tsichlas, Gerasimos Vonitsanos and Christos Zaroliagis
Algorithms 2022, 15(3), 96; https://doi.org/10.3390/a15030096 - 18 Mar 2022
Cited by 2 | Viewed by 2412
Abstract
In this work, we propose D3-Tree, a dynamic distributed deterministic structure for data management in decentralized networks, by engineering and extending an existing decentralized structure. Conducting an extensive experimental study, we verify that the implemented structure outperforms other well-known hierarchical tree-based [...] Read more.
In this work, we propose D3-Tree, a dynamic distributed deterministic structure for data management in decentralized networks, by engineering and extending an existing decentralized structure. Conducting an extensive experimental study, we verify that the implemented structure outperforms other well-known hierarchical tree-based structures since it provides better complexities regarding load-balancing operations. More specifically, the structure achieves an O(logN) amortized bound (N is the number of nodes present in the network), using an efficient deterministic load-balancing mechanism, which is general enough to be applied to other hierarchical tree-based structures. Moreover, our structure achieves O(logN) worst-case search performance. Last but not least, we investigate the structure’s fault tolerance, which hasn’t been sufficiently tackled in previous work, both theoretically and through rigorous experimentation. We prove that D3-Tree is highly fault-tolerant and achieves O(logN) amortized search cost under massive node failures, accompanied by a significant success rate. Afterwards, by incorporating this novel balancing scheme into the ART (Autonomous Range Tree) structure, we go one step further to achieve sub-logarithmic complexity and propose the ART+ structure. ART+ achieves an O(logb2logN) communication cost for query and update operations (b is a double-exponentially power of 2 and N is the total number of nodes). Moreover, ART+ is a fully dynamic and fault-tolerant structure, which supports the join/leave node operations in O(loglogN) expected WHP (with high proability) number of hops and performs load-balancing in O(loglogN) amortized cost. Full article
(This article belongs to the Collection Parallel and Distributed Computing: Algorithms and Applications)
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<p>The initial <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree structure (<b>middle</b>) and the operations of extension (<b>left</b>) and contraction (<b>right</b>).</p> Full article ">Figure 2
<p>Example of binary horizontal search with node failures.</p> Full article ">Figure 3
<p>Example of vertical search between <span class="html-italic">u</span> and unreachable <span class="html-italic">w</span>.</p> Full article ">Figure 4
<p>The ART<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math> structure for <span class="html-italic">b</span> = 2.</p> Full article ">Figure 5
<p>The <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree simulator user interface.</p> Full article ">Figure 6
<p>Node update operations. (<b>a</b>) average case, (<b>b</b>) worst case, (<b>c</b>) redistribution rate of winner <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree, (<b>d</b>) redistr/ion height of winner <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree.</p> Full article ">Figure 7
<p>Element update operations. (<b>a</b>) average messages, (<b>b</b>) load-balancing rate of winner <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree, (<b>c</b>) load-balancing height of winner <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree.</p> Full article ">Figure 8
<p>Single queries without/with node failures. (<b>a</b>) average messages without failures, (<b>b</b>) effect of massive failure, (<b>c</b>) average messages of <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree, (<b>d</b>) success percentage of <math display="inline"><semantics> <msup> <mi>D</mi> <mn>3</mn> </msup> </semantics></math>-Tree.</p> Full article ">Figure 9
<p>Cost of search operations. (<b>a</b>) Case <span class="html-italic">b</span> = 2, (<b>b</b>) case <span class="html-italic">b</span> = 4, (<b>c</b>) case <span class="html-italic">b</span> = 16, (<b>d</b>) massive failures.</p> Full article ">Figure 10
<p>Cost of load-balancing operation.</p> Full article ">
18 pages, 2598 KiB  
Article
Prediction of Harvest Time of Apple Trees: An RNN-Based Approach
by Tiago Boechel, Lucas Micol Policarpo, Gabriel de Oliveira Ramos, Rodrigo da Rosa Righi and Dhananjay Singh
Algorithms 2022, 15(3), 95; https://doi.org/10.3390/a15030095 - 18 Mar 2022
Cited by 10 | Viewed by 6714
Abstract
In the field of agricultural research, Machine Learning (ML) has been used to increase agricultural productivity and minimize its environmental impact, proving to be an essential technique to support decision making. Accurate harvest time prediction is a challenge for fruit production in a [...] Read more.
In the field of agricultural research, Machine Learning (ML) has been used to increase agricultural productivity and minimize its environmental impact, proving to be an essential technique to support decision making. Accurate harvest time prediction is a challenge for fruit production in a sustainable manner, which could eventually reduce food waste. Linear models have been used to estimate period duration; however, they present variability when used to estimate the chronological time of apple tree stages. This study proposes the PredHarv model, which is a machine learning model that uses Recurrent Neural Networks (RNN) to predict the start date of the apple harvest, given the weather conditions related to the temperature expected for the period. Predictions are made from the phenological phase of the beginning of flowering, using a multivariate approach, based on the time series of phenology and meteorological data. The computational model contributes to anticipating information about the harvest date, enabling the grower to better plan activities, avoiding costs, and consequently improving productivity. We developed a prototype of the model and performed experiments with real datasets from agricultural institutions. We evaluated the metrics, and the results obtained in evaluation scenarios demonstrate that the model is efficient, has good generalizability, and is capable of improving the accuracy of the prediction results. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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<p>Apple phenologial stages.</p> Full article ">Figure 2
<p>PredHarv model architecture.</p> Full article ">Figure 3
<p>Timeline of the prediction process.</p> Full article ">Figure 4
<p>Processing flow. (<b>a</b>) Training step. (<b>b</b>) Prediction step.</p> Full article ">Figure 5
<p>DS1 input variables boxplot.</p> Full article ">Figure 6
<p>Feature correlation heatmap.</p> Full article ">Figure 7
<p>K-fold cross-validation with k = 5.</p> Full article ">Figure 8
<p>Dynamics of the predictions obtained with the PredHarv model.</p> Full article ">Figure 9
<p>PredHarv model and linear model prediction results—DS1 dataset.</p> Full article ">Figure 10
<p>PredHarv model and linear model prediction results—DS2 dataset.</p> Full article ">
16 pages, 1615 KiB  
Article
Mechanical Fault Prognosis through Spectral Analysis of Vibration Signals
by Kang Wang, Zhi-Jiang Xu, Yi Gong and Ke-Lin Du
Algorithms 2022, 15(3), 94; https://doi.org/10.3390/a15030094 - 15 Mar 2022
Cited by 2 | Viewed by 3097
Abstract
Vibration signal analysis is the most common technique used for mechanical vibration monitoring. By using vibration sensors, the fault prognosis of rotating machinery provides a way to detect possible machine damage at an early stage and prevent property losses by taking appropriate measures. [...] Read more.
Vibration signal analysis is the most common technique used for mechanical vibration monitoring. By using vibration sensors, the fault prognosis of rotating machinery provides a way to detect possible machine damage at an early stage and prevent property losses by taking appropriate measures. We first propose a digital integrator in frequency domain by combining fast Fourier transform with digital filtering. The velocity and displacement signals are, respectively, obtained from an acceleration signal by means of two digital integrators. We then propose a fast method for the calculation of the envelope spectra and instantaneous frequency by using the spectral properties of the signals. Cepstrum is also introduced in order to detect the unidentifiable periodic signal in the power spectrum. Further, a fault prognosis algorithm is presented by exploiting these spectral analyses. Finally, we design and implement a visualized real-time vibration analyzer on a Raspberry Pi embedded system, where our fault prognosis algorithm is the core algorithm. The real-time signals of acceleration, velocity, displacement of vibration, as well as their corresponding spectra and statistics, are visualized. The developed fault prognosis system has been successfully deployed in a water company. Full article
(This article belongs to the Special Issue 1st Online Conference on Algorithms (IOCA2021))
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<p>Block diagram of the test platform.</p> Full article ">Figure 2
<p>Software flow of the vibration analysis.</p> Full article ">Figure 3
<p>Real-time monitoring GUI for Raspberry Pi-based vibration test platform.</p> Full article ">Figure 4
<p>The side bands in simulated gearbox vibration signals by using cepstrum analysis.</p> Full article ">Figure 5
<p>Measurement settings interface.</p> Full article ">Figure 6
<p>Water pump room of a water supply company with seven large-scale pumps, including gearboxes and water pipes.</p> Full article ">
19 pages, 1242 KiB  
Article
Ensemble Machine Learning Model to Predict the Waterborne Syndrome
by Mohammed Gollapalli
Algorithms 2022, 15(3), 93; https://doi.org/10.3390/a15030093 - 11 Mar 2022
Cited by 18 | Viewed by 3799
Abstract
The COVID-19 epidemic has highlighted the significance of sanitization and maintaining hygienic access to clean water to reduce mortality and morbidity cases worldwide. Diarrhea is one of the prevalent waterborne diseases caused due to contaminated water in many low-income countries with similar living [...] Read more.
The COVID-19 epidemic has highlighted the significance of sanitization and maintaining hygienic access to clean water to reduce mortality and morbidity cases worldwide. Diarrhea is one of the prevalent waterborne diseases caused due to contaminated water in many low-income countries with similar living conditions. According to the latest statistics from the World Health Organization (WHO), diarrhea is among the top five primary causes of death worldwide in low-income nations. The condition affects people in every age group due to a lack of proper water used for daily living. In this study, a stacking ensemble machine learning model was employed against traditional models to extract clinical knowledge for better understanding patients’ characteristics; disease prevalence; hygienic conditions; quality of water used for cooking, bathing, and toiletries; chemicals used; therapist’s medications; and symptoms that are reflected in the field study data. Results revealed that the ensemble model provides higher accuracy with 98.90% as part of training and testing phases when experimented against frequently used J48, Naïve Bayes, SVM, NN, PART, Random Forest, and Logistic Regression models. Managing outcomes of this research in the early stages could assist people in low-income countries to have a better lifestyle, fewer infections, and minimize expensive hospital visits. Full article
(This article belongs to the Special Issue Algorithms for Feature Selection)
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<p>Three stages of the knowledge extraction process employed in the research.</p> Full article ">Figure 2
<p>Performance of ensemble model against traditional classifiers.</p> Full article ">Figure 3
<p>Kappa statistics of experimented classifiers against ensemble model.</p> Full article ">Figure 4
<p>Prevalence of disease against genders.</p> Full article ">Figure 5
<p>Repetition of disease among age groups for the 1st, 2nd, 3rd, and beyond.</p> Full article ">
16 pages, 1444 KiB  
Article
Mean Estimation on the Diagonal of Product Manifolds
by Mathias Højgaard Jensen and Stefan Sommer
Algorithms 2022, 15(3), 92; https://doi.org/10.3390/a15030092 - 10 Mar 2022
Cited by 2 | Viewed by 2784
Abstract
Computing sample means on Riemannian manifolds is typically computationally costly, as exemplified by computation of the Fréchet mean, which often requires finding minimizing geodesics to each data point for each step of an iterative optimization scheme. When closed-form expressions for geodesics are not [...] Read more.
Computing sample means on Riemannian manifolds is typically computationally costly, as exemplified by computation of the Fréchet mean, which often requires finding minimizing geodesics to each data point for each step of an iterative optimization scheme. When closed-form expressions for geodesics are not available, this leads to a nested optimization problem that is costly to solve. The implied computational cost impacts applications in both geometric statistics and in geometric deep learning. The weighted diffusion mean offers an alternative to the weighted Fréchet mean. We show how the diffusion mean and the weighted diffusion mean can be estimated with a stochastic simulation scheme that does not require nested optimization. We achieve this by conditioning a Brownian motion in a product manifold to hit the diagonal at a predetermined time. We develop the theoretical foundation for the sampling-based mean estimation, we develop two simulation schemes, and we demonstrate the applicability of the method with examples of sampled means on two manifolds. Full article
(This article belongs to the Special Issue Stochastic Algorithms and Their Applications)
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<p>(<b>left</b>) The mean estimator viewed as a projection onto the diagonal of a product manifold. Given a set <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>∈</mo> <mi>M</mi> </mrow> </semantics></math>, the tuple <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </semantics></math> (blue dot) belongs to the product manifold <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>×</mo> <mo>⋯</mo> <mo>×</mo> <mi>M</mi> </mrow> </semantics></math>. The mean estimator <math display="inline"><semantics> <mover accent="true"> <mi>μ</mi> <mo>^</mo> </mover> </semantics></math> can be identified with the projection of <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </semantics></math> onto the diagonal <span class="html-italic">N</span> (red dot). (<b>right</b>) Diffusion mean estimator in <math display="inline"><semantics> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </semantics></math> using Brownian bridges conditioned on the diagonal. Here a Brownian bridge <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>X</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> in <math display="inline"><semantics> <msup> <mi mathvariant="double-struck">R</mi> <mn>8</mn> </msup> </semantics></math> is conditioned on hitting the diagonal <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>⊆</mo> <msup> <mi mathvariant="double-struck">R</mi> <mn>8</mn> </msup> </mrow> </semantics></math> at time <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>. The components <math display="inline"><semantics> <msub> <mi>X</mi> <mi>j</mi> </msub> </semantics></math> each being two-dimensional processes are shown in the plot.</p> Full article ">Figure 2
<p>The mean estimator viewed as a projection onto the diagonal of a product manifold. Conditioning on the closest point in the diagonal yields a density on the diagonal depending on the time to arrival <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>. As <span class="html-italic">T</span> tends to zero the density convergence to the Dirac-delta distribution (grey), whereas as <span class="html-italic">T</span> increases the variance of the distribution increases (rouge).</p> Full article ">Figure 3
<p>3 points on <math display="inline"><semantics> <msup> <mi mathvariant="double-struck">S</mi> <mn>2</mn> </msup> </semantics></math> together with a sample mean (red) and the diagonal process in <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <msup> <mi mathvariant="double-struck">S</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mi>n</mi> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> conditioned on the diagonal.</p> Full article ">Figure 4
<p>(<b>left</b>) 256 sampled data points on <math display="inline"><semantics> <msup> <mi mathvariant="double-struck">S</mi> <mn>2</mn> </msup> </semantics></math> (north pole being population mean). (<b>right</b>) 32 samples of the diffusion mean conditioned on the diagonal of <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <msup> <mi mathvariant="double-struck">S</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mi>n</mi> </msup> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>256</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>. As can be seen, the variation in the mean samples is limited.</p> Full article ">Figure 5
<p>(<b>left</b>) One configuration of 17 landmarks overlayed the MR image from which the configuration was annotated. (<b>right</b>) All 14 landmark configurations plotted together (one color for each configuration of 17 landmarks).</p> Full article ">Figure 6
<p>Samples from the diagonal process with <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (<b>right</b>). The effect of varying the Brownian motion end time <span class="html-italic">T</span> is clearly visible.</p> Full article ">Figure 7
<p>One sampled diffusion mean with the sampling scheme (blue configuration) together with estimated Fréchet mean (green configuration). The forward sampling scheme is significantly faster than the iterative optimization needed for the Fréchet mean on the landmark manifold where closed-form solutions of the geodesic equations are not available.</p> Full article ">
14 pages, 519 KiB  
Article
Analysis of Explainable Goal-Driven Reinforcement Learning in a Continuous Simulated Environment
by Ernesto Portugal, Francisco Cruz, Angel Ayala and Bruno Fernandes
Algorithms 2022, 15(3), 91; https://doi.org/10.3390/a15030091 - 9 Mar 2022
Cited by 6 | Viewed by 3168
Abstract
Currently, artificial intelligence is in an important period of growth. Due to the technology boom, it is now possible to solve problems that could not be resolved previously. For example, through goal-driven learning, it is possible that intelligent machines or agents may be [...] Read more.
Currently, artificial intelligence is in an important period of growth. Due to the technology boom, it is now possible to solve problems that could not be resolved previously. For example, through goal-driven learning, it is possible that intelligent machines or agents may be able to perform tasks without human intervention. However, this also leads to the problem of understanding the agent’s decision making. Therefore, explainable goal-driven learning attempts to eliminate this gap. This work focuses on the adaptability of two explainability methods in continuous environments. The methods based on learning and introspection proposed a probability value for success to explain the agent’s behavior. These had already been tested in discrete environments. The continuous environment used in this study is the car-racing problem. This is a simulated car racing game that forms part of the Python Open AI Gym Library. The agents in this environment were trained with the Deep Q-Network algorithm, and in parallel the explainability methods were implemented. This research included a proposal for carrying out the adaptation and implementation of these methods in continuous states. The adaptation of the learning method produced major changes, implemented through an artificial neural network. The obtained probabilities of both methods were consistent throughout the experiments. The probability result was greater in the learning method. In terms of computational resources, the introspection method was slightly better than its counterpart. Full article
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<p>Diagram of the neural network used to calculate the Q-values using the DQN algorithm and the probability of success using the learning-based method. When computing the probability of success, the neural architecture used a sigmoid activation function in the last dense layer in order to restrict the output values between 0 and 1. Three consecutive <math display="inline"><semantics> <mrow> <mn>96</mn> <mo>×</mo> <mn>96</mn> </mrow> </semantics></math> gray images of the car racing game are used as inputs.</p> Full article ">Figure 2
<p>Experimental scenario. In the image from left to right, colors depict velocity (white), the four ABS sensors (blue and purple), the position of the steering wheel (green), and the gyroscope (red).</p> Full article ">Figure 3
<p>The input is represented by three consecutive images of <math display="inline"><semantics> <mrow> <mn>96</mn> <mo>×</mo> <mn>96</mn> </mrow> </semantics></math> (matrix of <math display="inline"><semantics> <mrow> <mn>96</mn> <mo>×</mo> <mn>96</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math>) from the car racing game. The images in the figure are examples since they were previously processed in a gray scale.</p> Full article ">Figure 4
<p>Averaged Q-values for five runs using the DQN algorithm during 500 episodes. The Q-values are averaged for each episode considering twelve possible actions. The results are smoothed in a window of 30 data using a linear convolution.</p> Full article ">Figure 5
<p>Total reward for five runs using the DQN algorithm during 500 episodes. In the figure, the collected rewards are smoothed in a window of 30 data using a linear convolution.</p> Full article ">Figure 6
<p>Average value of the probability of success for five runs of the agent’s training during 500 episodes using the learning-based method proposed in Algorithm 1. The probability value is smoothed and the shaded area refers to the standard deviation.</p> Full article ">Figure 7
<p>Average values for the probability of success for five runs of the agent’s training during 500 episodes using the introspection-based method proposed in Algorithm 2. The probability value is smoothed and the shaded area represents the standard deviation.</p> Full article ">Figure 8
<p>Values for use of resources considering RAM memory and percentage of processor use (CPU). Average value and standard deviation are computed for three training processes during 200 episodes for each method. The y axis on the left relates to the gigabyte scale, and the percentage is on the right. A lower standard deviation is shown for the introspection method for memory use. This indicates greater stability using this resource. For the case of the CPU, both methods maintained a not null standard deviation close to 0.</p> Full article ">
24 pages, 2603 KiB  
Article
Kleene Algebra to Compute Invariant Sets of Dynamical Systems
by Thomas Le Mézo, Luc Jaulin, Damien Massé and Benoit Zerr
Algorithms 2022, 15(3), 90; https://doi.org/10.3390/a15030090 - 8 Mar 2022
Cited by 2 | Viewed by 2721
Abstract
In this paper, we show that a basic fixed point method used to enclose the greatest fixed point in a Kleene algebra will allow us to compute inner and outer approximations of invariant-based sets for continuous-time nonlinear dynamical systems. Our contribution is to [...] Read more.
In this paper, we show that a basic fixed point method used to enclose the greatest fixed point in a Kleene algebra will allow us to compute inner and outer approximations of invariant-based sets for continuous-time nonlinear dynamical systems. Our contribution is to provide the definitions and theorems that will allow us to make the link between the theory of invariant sets and the Kleene algebra. This link has never be done before and will allow us to compute rigorously sets that can be defined as a combination of positive invariant sets. Some illustrating examples show the nice properties of the approach. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
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<p>The grid corresponds to the machine lattice <math display="inline"><semantics> <msub> <mi mathvariant="script">L</mi> <mi>M</mi> </msub> </semantics></math> associated to the lattice <math display="inline"><semantics> <mi mathvariant="script">L</mi> </semantics></math>.</p> Full article ">Figure 2
<p>Fixed points <math display="inline"><semantics> <mrow> <mi>Fix</mi> <mfenced separators="" open="(" close=")"> <msup> <mfenced separators="" open="(" close=")"> <msup> <mi>f</mi> <mo>−</mo> </msup> </mfenced> <mo>∗</mo> </msup> </mfenced> </mrow> </semantics></math> in magenta, <math display="inline"><semantics> <mrow> <mi>Fix</mi> <mfenced separators="" open="(" close=")"> <msup> <mfenced separators="" open="(" close=")"> <msup> <mi>f</mi> <mo>+</mo> </msup> </mfenced> <mo>∗</mo> </msup> </mfenced> </mrow> </semantics></math> in blue, and <math display="inline"><semantics> <mrow> <mi>Fix</mi> <mfenced separators="" open="(" close=")"> <msup> <mi>f</mi> <mo>∗</mo> </msup> </mfenced> </mrow> </semantics></math> is the light red polygon.</p> Full article ">Figure 3
<p>Algorithm that computes an approximation of <math display="inline"><semantics> <mrow> <msup> <mi>f</mi> <mo>∗</mo> </msup> <mfenced open="(" close=")"> <mi>a</mi> </mfenced> <mo>,</mo> <mi>a</mi> <mo>∈</mo> <mfenced open="[" close="]"> <mi>a</mi> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>Illustration of the definition of a path inside a region.</p> Full article ">Figure 5
<p>Forward Eulerian predictor <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>f</mi> <mo>→</mo> </mover> <mfenced open="(" close=")"> <mi mathvariant="double-struck">A</mi> </mfenced> </mrow> </semantics></math> eliminating points that will escape from <math display="inline"><semantics> <mi mathvariant="double-struck">A</mi> </semantics></math>.</p> Full article ">Figure 6
<p>An inconsistent situation that can never occur where <math display="inline"><semantics> <mrow> <mi mathvariant="bold">a</mi> <mo>∈</mo> <msup> <mi>Inv</mi> <mo>+</mo> </msup> <mfenced open="(" close=")"> <mi mathvariant="double-struck">A</mi> </mfenced> <mspace width="4.pt"/> <mi>but</mi> <mspace width="4.pt"/> <mi mathvariant="bold">a</mi> <mo>∉</mo> <msup> <mover accent="true"> <mrow> <mi>f</mi> <mspace width="0.166667em"/> </mrow> <mo>→</mo> </mover> <mo>∗</mo> </msup> <mfenced open="(" close=")"> <mi mathvariant="double-struck">A</mi> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>An impossible situation where <math display="inline"><semantics> <mrow> <mi mathvariant="bold">a</mi> <mo>∉</mo> <msup> <mi>Inv</mi> <mo>+</mo> </msup> <mfenced open="(" close=")"> <mi mathvariant="double-struck">A</mi> </mfenced> <mspace width="4.pt"/> <mi>but</mi> <mspace width="4.pt"/> <mi mathvariant="bold">a</mi> <mo>∈</mo> <msup> <mover accent="true"> <mrow> <mi>f</mi> <mspace width="0.166667em"/> </mrow> <mo>→</mo> </mover> <mo>∗</mo> </msup> <mfenced open="(" close=")"> <mi mathvariant="double-struck">A</mi> </mfenced> </mrow> </semantics></math> that is used in the proof of Theorem 4.</p> Full article ">Figure 8
<p>Approximation of the greatest negative invariant set included in the frame box <math display="inline"><semantics> <mi mathvariant="double-struck">A</mi> </semantics></math>.</p> Full article ">Figure 9
<p>Forward reach set associated with the red disk <math display="inline"><semantics> <mi mathvariant="double-struck">A</mi> </semantics></math> for an infinite time horizon.</p> Full article ">Figure 10
<p>Forward reach set associated with the red disk <math display="inline"><semantics> <mi mathvariant="double-struck">A</mi> </semantics></math>.</p> Full article ">Figure 11
<p>Inner and outer approximation of the control forward reach set.</p> Full article ">Figure 12
<p>Approximation of the smallest positive invariant set containing <math display="inline"><semantics> <mn mathvariant="bold">0</mn> </semantics></math>.</p> Full article ">Figure 13
<p>Paths starting from <math display="inline"><semantics> <mi mathvariant="double-struck">A</mi> </semantics></math>, avoiding <math display="inline"><semantics> <mi mathvariant="double-struck">B</mi> </semantics></math>, and reaching <math display="inline"><semantics> <mi mathvariant="double-struck">C</mi> </semantics></math>.</p> Full article ">
17 pages, 2404 KiB  
Article
A Contrastive Learning Method for the Visual Representation of 3D Point Clouds
by Feng Zhu, Jieyu Zhao and Zhengyi Cai
Algorithms 2022, 15(3), 89; https://doi.org/10.3390/a15030089 - 8 Mar 2022
Cited by 2 | Viewed by 2749
Abstract
At present, the unsupervised visual representation learning of the point cloud model is mainly based on generative methods, but the generative methods pay too much attention to the details of each point, thus ignoring the learning of semantic information. Therefore, this paper proposes [...] Read more.
At present, the unsupervised visual representation learning of the point cloud model is mainly based on generative methods, but the generative methods pay too much attention to the details of each point, thus ignoring the learning of semantic information. Therefore, this paper proposes a discriminative method for the contrastive learning of three-dimensional point cloud visual representations, which can effectively learn the visual representation of point cloud models. The self-attention point cloud capsule network is designed as the backbone network, which can effectively extract the features of point cloud data. By compressing the digital capsule layer, the class dependence of features is eliminated, and the generalization ability of the model and the ability of feature queues to store features are improved. Aiming at the equivariance of the capsule network, the Jaccard loss function is constructed, which is conducive to the network distinguishing the characteristics of positive and negative samples, thereby improving the performance of the contrastive learning. The model is pre-trained on the ShapeNetCore data set, and the pre-trained model is used for classification and segmentation tasks. The classification accuracy on the ModelNet40 data set is 0.1% higher than that of the best unsupervised method, PointCapsNet, and when only 10% of the label data is used, the classification accuracy exceeds 80%. The mIoU of part segmentation on the ShapeNet data set is 1.2% higher than the best comparison method, MulUnsupervised. The experimental results of classification and segmentation show that the proposed method has good performance in accuracy. The alignment and uniformity of features are better than the generative method of PointCapsNet, which proves that this method can learn the visual representation of the three-dimensional point cloud model more effectively. Full article
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<p>Contrastive learning framework.</p> Full article ">Figure 2
<p>The equivariance of the capsule network.</p> Full article ">Figure 3
<p>Self-attention point cloud capsule network.</p> Full article ">Figure 4
<p>The generative method, PointCapsNet.</p> Full article ">Figure 5
<p>The method described in this article.</p> Full article ">Figure 6
<p>SVM classification accuracy and the number of labeled samples.</p> Full article ">Figure 7
<p>The visualized results of part segmentation.</p> Full article ">Figure 8
<p>Multiple data augmentation methods.</p> Full article ">
16 pages, 791 KiB  
Article
Research on Agricultural Machinery Rental Optimization Based on the Dynamic Artificial Bee-Ant Colony Algorithm
by Jialin Hou, Jingtao Zhang, Wanying Wu, Tianguo Jin and Kai Zhou
Algorithms 2022, 15(3), 88; https://doi.org/10.3390/a15030088 - 8 Mar 2022
Cited by 6 | Viewed by 3723
Abstract
Agricultural machinery rental is a new service form that uses big data in agriculture to improve the utilization rate of agricultural machinery and promote the development of the agricultural economy. To realize agricultural machinery scheduling optimization in cloud services, a dynamic artificial bee-ant [...] Read more.
Agricultural machinery rental is a new service form that uses big data in agriculture to improve the utilization rate of agricultural machinery and promote the development of the agricultural economy. To realize agricultural machinery scheduling optimization in cloud services, a dynamic artificial bee-ant colony algorithm (DABAA) is proposed to solve the above problem. First, to improve the practicability of the mathematical model in agricultural production, a dynamic coefficient is proposed. Then the mutation operation is combined with the artificial bee colony (ABC) algorithm to improve the algorithm. Then, iterative threshold adjustment and optimal fusion point evaluation are used to combine the ABC algorithm with the ant colony optimization (ACO) algorithm, which not only improves the search precision but also improves the running speed. Finally, two groups of comparison experiments are carried out, and the results show that the DABAA can obviously improve the running speed and accuracy of cloud services in agricultural machinery rental. Full article
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<p>Multitasking composition process.</p> Full article ">Figure 2
<p>DABAA flow chart.</p> Full article ">Figure 3
<p>Process of optimization.</p> Full article ">Figure 4
<p>Route of multiple agricultural machine rental.</p> Full article ">Figure 5
<p>Results of accuracy with different task sizes.</p> Full article ">Figure 6
<p>Boxplot of QoS fitness values.</p> Full article ">Figure 7
<p>Average time consumption.</p> Full article ">
32 pages, 4929 KiB  
Article
A Seed-Guided Latent Dirichlet Allocation Approach to Predict the Personality of Online Users Using the PEN Model
by Saravanan Sagadevan, Nurul Hashimah Ahamed Hassain Malim and Mohd Heikal Husin
Algorithms 2022, 15(3), 87; https://doi.org/10.3390/a15030087 - 8 Mar 2022
Cited by 4 | Viewed by 3158
Abstract
There is a growing interest in topic modeling to decipher the valuable information embedded in natural texts. However, there are no studies training an unsupervised model to automatically categorize the social networks (SN) messages according to personality traits. Most of the existing literature [...] Read more.
There is a growing interest in topic modeling to decipher the valuable information embedded in natural texts. However, there are no studies training an unsupervised model to automatically categorize the social networks (SN) messages according to personality traits. Most of the existing literature relied on the Big 5 framework and psychological reports to recognize the personality of users. Furthermore, collecting datasets for other personality themes is an inherent problem that requires unprecedented time and human efforts, and it is bounded with privacy constraints. Alternatively, this study hypothesized that a small set of seed words is enough to decipher the psycholinguistics states encoded in texts, and the auxiliary knowledge could synergize the unsupervised model to categorize the messages according to human traits. Therefore, this study devised a dataless model called Seed-guided Latent Dirichlet Allocation (SLDA) to categorize the SN messages according to the PEN model that comprised Psychoticism, Extraversion, and Neuroticism traits. The intrinsic evaluations were conducted to determine the performance and disclose the nature of texts generated by SLDA, especially in the context of Psychoticism. The extrinsic evaluations were conducted using several machine learning classifiers to posit how well the topic model has identified latent semantic structure that persists over time in the training documents. The findings have shown that SLDA outperformed other models by attaining a coherence score up to 0.78, whereas the machine learning classifiers can achieve precision up to 0.993. We also will be shared the corpus generated by SLDA for further empirical studies. Full article
(This article belongs to the Special Issue Ensemble Algorithms and/or Explainability)
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<p>Research Methodology.</p> Full article ">Figure 2
<p>Probability distribution of the top 30 words.</p> Full article ">Figure 3
<p>Word distribution of Neuroticism and Extraversion for <span class="html-italic">myPersonality</span> and <span class="html-italic">Sentiment140</span>.</p> Full article ">Figure 3 Cont.
<p>Word distribution of Neuroticism and Extraversion for <span class="html-italic">myPersonality</span> and <span class="html-italic">Sentiment140</span>.</p> Full article ">Figure 4
<p>Word distribution of one vs. all distribution for <span class="html-italic">myPersonality</span> and <span class="html-italic">Sentiment140</span>.</p> Full article ">Figure 5
<p><span class="html-italic">t-SNE</span> visualization for multiclass distribution of <span class="html-italic">myPersonality</span> (<b>a</b>) and <span class="html-italic">Sentiment140</span> (<b>b</b>).</p> Full article ">Figure 6
<p><span class="html-italic">t-SNE</span> visualization for one vs. all distribution of <span class="html-italic">myPersonality</span> (<b>a</b>) and <span class="html-italic">Sentiment140</span> (<b>b</b>).</p> Full article ">Figure 7
<p>Confusion Matrix of one vs. all Classification.</p> Full article ">Figure 7 Cont.
<p>Confusion Matrix of one vs. all Classification.</p> Full article ">Figure 8
<p>Confusion Matrix of Multiclass Classification.</p> Full article ">
14 pages, 13263 KiB  
Article
Prediction of Intrinsically Disordered Proteins Using Machine Learning Based on Low Complexity Methods
by Xingming Zeng, Haiyuan Liu and Hao He
Algorithms 2022, 15(3), 86; https://doi.org/10.3390/a15030086 - 8 Mar 2022
Cited by 1 | Viewed by 2624
Abstract
Prediction of intrinsic disordered proteins is a hot area in the field of bio-information. Due to the high cost of evaluating the disordered regions of protein sequences using experimental methods, we used a low-complexity prediction scheme. Sequence complexity is used in this scheme [...] Read more.
Prediction of intrinsic disordered proteins is a hot area in the field of bio-information. Due to the high cost of evaluating the disordered regions of protein sequences using experimental methods, we used a low-complexity prediction scheme. Sequence complexity is used in this scheme to calculate five features for each residue of the protein sequence, including the Shannon entropy, the Topo-logical entropy, the Permutation entropy and the weighted average values of two propensities. Particularly, this is the first time that permutation entropy has been applied to the field of protein sequencing. In addition, in the data preprocessing stage, an appropriately sized sliding window and a comprehensive oversampling scheme can be used to improve the prediction performance of our scheme, and two ensemble learning algorithms are also used to verify the prediction results before and after. The results show that adding permutation entropy improves the performance of the prediction algorithm, in which the MCC value can be improved from the original 0.465 to 0.526 in our scheme, proving its universality. Finally, we compare the simulation results of our scheme with those of some existing schemes to demonstrate its effectiveness. Full article
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<p>Calculation process of permutation entropy.</p> Full article ">Figure 2
<p>Scheme specific flow chart.</p> Full article ">Figure 3
<p>Probability distribution diagram.</p> Full article ">Figure 4
<p>The importance of five features in the algorithm.</p> Full article ">Figure 5
<p>Different window size performance in GBDT.</p> Full article ">Figure 6
<p>Different window size performance in LightGBM.</p> Full article ">Figure 7
<p>Remark465 and Permutation entropy before and after windowing.</p> Full article ">Figure 8
<p>The prediction result of IAPP based on our system.</p> Full article ">Figure 9
<p>The prediction result of IAPP based on DisPort.</p> Full article ">
12 pages, 1291 KiB  
Article
Dynamic Layout Design Optimization to Improve Patient Flow in Outpatient Clinics Using Genetic Algorithms
by Jyoti R. Munavalli, Shyam Vasudeva Rao, Aravind Srinivasan and Frits Van Merode
Algorithms 2022, 15(3), 85; https://doi.org/10.3390/a15030085 - 6 Mar 2022
Cited by 5 | Viewed by 3962
Abstract
Evolutionary algorithms, such as genetic algorithms have been used in various optimization problems. In this paper, we propose to apply this algorithm to obtain the layout design/redesign in order to improve the patient flow in an outpatient clinic. Layout designs are planned considering [...] Read more.
Evolutionary algorithms, such as genetic algorithms have been used in various optimization problems. In this paper, we propose to apply this algorithm to obtain the layout design/redesign in order to improve the patient flow in an outpatient clinic. Layout designs are planned considering long-term requirements whereas the layout keeps modifying as per short-term demands. Over a period of time, the layout often does not remain efficient. Therefore, there is a need for such a model that helps in decision making on layout redesigns, and it must also optimize workflow by incorporating the flow constraints. In this study, we propose to minimize the waiting times by obtaining optimal and sub-optimal layout designs. A genetic algorithm is implemented to redesign the layouts based on the changing dynamics of patient demand, clinical pathways and services offered. The workflow is simulated with current layout and optimized layouts, and the results in terms of waiting time and cycle time are compared. The study shows that when layout design or redesign incorporate the workflow and pathways along with associated constraints, improves waiting time and cycle time of patients in the outpatient clinic. The distance between the departments/locations is translated to travelling time and overall travel distance/time is minimized by rearranging the allocations of departments to the location through genetic algorithms. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms and Applications)
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<p>Outpatient clinic workflow of Aravind Eye OPC (created based on observations).</p> Full article ">Figure 2
<p>Gene representation in terms of locations and departments.</p> Full article ">Figure 3
<p>Crossover and Mutations.</p> Full article ">Figure 4
<p>Complete optimization model.</p> Full article ">Figure 5
<p>Layout redesigns obtained from Genetic Algorithm.</p> Full article ">Figure 6
<p>Layout of the OPC showing locations and assigned departments.</p> Full article ">
16 pages, 4969 KiB  
Article
Eye Fatigue Detection through Machine Learning Based on Single Channel Electrooculography
by Yuqi Wang, Lijun Zhang and Zhen Fang
Algorithms 2022, 15(3), 84; https://doi.org/10.3390/a15030084 - 3 Mar 2022
Cited by 8 | Viewed by 4346
Abstract
Nowadays, eye fatigue is becoming more common globally. However, there was no objective and effective method for eye fatigue detection except the sample survey questionnaire. An eye fatigue detection method by machine learning based on the Single-Channel Electrooculography-based System is proposed. Subjects are [...] Read more.
Nowadays, eye fatigue is becoming more common globally. However, there was no objective and effective method for eye fatigue detection except the sample survey questionnaire. An eye fatigue detection method by machine learning based on the Single-Channel Electrooculography-based System is proposed. Subjects are required to finish the industry-standard questionnaires of eye fatigue; the results are used as data labels. Then, we collect their electrooculography signals through a single-channel device. From the electrooculography signals, the five most relevant feature values of eye fatigue are extracted. A machine learning model that uses the five feature values as its input is designed for eye fatigue detection. Experimental results show that there is an objective link between electrooculography and eye fatigue. This method could be used in daily eye fatigue detection and it is promised in the future. Full article
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<p>The change of EOG in right eye movement.</p> Full article ">Figure 2
<p>The change of EOG in left eye movement.</p> Full article ">Figure 3
<p>Schematic diagram of the EOG measurement.</p> Full article ">Figure 4
<p>System block diagram of EOG measurement.</p> Full article ">Figure 5
<p>Display terminal visual fatigue test and evaluation method part 2 scale evaluation method [<a href="#B13-algorithms-15-00084" class="html-bibr">13</a>].</p> Full article ">Figure 5 Cont.
<p>Display terminal visual fatigue test and evaluation method part 2 scale evaluation method [<a href="#B13-algorithms-15-00084" class="html-bibr">13</a>].</p> Full article ">Figure 6
<p>Eye fatigue experiment process.</p> Full article ">Figure 7
<p>Comparison of raw EOG signal and processed EOG signal.</p> Full article ">Figure 8
<p>(<b>a</b>) The extracted features as a directed graphical. (<b>b</b>) Correlation ranking of all features.</p> Full article ">Figure 8 Cont.
<p>(<b>a</b>) The extracted features as a directed graphical. (<b>b</b>) Correlation ranking of all features.</p> Full article ">Figure 9
<p>(<b>a</b>) The 5 selected features as a directed graphical. (<b>b</b>) Correlation ranking of the 5 selected features.</p> Full article ">Figure 9 Cont.
<p>(<b>a</b>) The 5 selected features as a directed graphical. (<b>b</b>) Correlation ranking of the 5 selected features.</p> Full article ">Figure 10
<p>Welch spectral estimation of the denoised signal (<a href="#algorithms-15-00084-f007" class="html-fig">Figure 7</a>b).</p> Full article ">Figure 11
<p>Eye movement signal recognition (red+ indicates right movement, red* indicates left movement).</p> Full article ">Figure 12
<p>The structure of the pruned classification decision tree.</p> Full article ">
12 pages, 916 KiB  
Article
Detection of Insulators on Power Transmission Line Based on an Improved Faster Region-Convolutional Neural Network
by Haijian Hu, Yicen Liu and Haina Rong
Algorithms 2022, 15(3), 83; https://doi.org/10.3390/a15030083 - 1 Mar 2022
Cited by 6 | Viewed by 3106
Abstract
Detecting insulators on a power transmission line is of great importance for the safe operation of power systems. Aiming at the problem of the missed detection and misjudgment of the original feature extraction network VGG16 of a faster region-convolutional neural network (R-CNN) in [...] Read more.
Detecting insulators on a power transmission line is of great importance for the safe operation of power systems. Aiming at the problem of the missed detection and misjudgment of the original feature extraction network VGG16 of a faster region-convolutional neural network (R-CNN) in the face of insulators of different sizes, in order to improve the accuracy of insulators’ detection on power transmission lines, an improved faster R-CNN algorithm is proposed. The improved algorithm replaces the original backbone feature extraction network VGG16 in faster R-CNN with the Resnet50 network with deeper layers and a more complex structure, adding an efficient channel attention module based on the channel attention mechanism. Experimental results show that the feature extraction performance has been effectively improved through the improvement of the backbone feature extraction network. The network model is trained on a training set consisting of 6174 insulator pictures, and is tested on a testing set consisting of 686 pictures. Compared with the traditional faster R-CNN, the mean average precision of the improved faster R-CNN increases to 89.37%, with an improvement of 1.63%. Full article
(This article belongs to the Topic Soft Computing)
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<p>Faster R-CNN network structure diagram.</p> Full article ">Figure 2
<p>Aerial images of insulators on different backgrounds.</p> Full article ">Figure 3
<p>Insulator true label frame and prediction frame.</p> Full article ">Figure 4
<p>Precision–recall curve.</p> Full article ">Figure 5
<p>Training loss under the VGG16 backbone network.</p> Full article ">Figure 6
<p>Training loss under the Resnet50 backbone network.</p> Full article ">Figure 7
<p>Training loss under the ECA-net+Resnet50 backbone network.</p> Full article ">Figure 8
<p>Precision–recall curve graph under the VGG16 backbone network.</p> Full article ">Figure 9
<p>Precision–recall curve graph under the Resnet50 backbone network.</p> Full article ">Figure 10
<p>Precision–recall curve graph under the ECA-net+Resnet50 backbone network.</p> Full article ">Figure 11
<p>Insulator test results of the improved faster R-CNN.</p> Full article ">
14 pages, 1372 KiB  
Review
Non-Invasive Systems and Methods Patents Review Based on Electrocardiogram for Diagnosis of Cardiovascular Diseases
by Nellyzeth Flores, Marco A. Reyna, Roberto L. Avitia, Jose Antonio Cardenas-Haro and Conrado Garcia-Gonzalez
Algorithms 2022, 15(3), 82; https://doi.org/10.3390/a15030082 - 28 Feb 2022
Cited by 3 | Viewed by 3009
Abstract
Cardiovascular disease (CVD) is a global public health problem. It is a disease of multifactorial origin, and with this characteristic, having an accurate diagnosis of its incidence is a problem that health personnel face every day. That is why having all the indispensable [...] Read more.
Cardiovascular disease (CVD) is a global public health problem. It is a disease of multifactorial origin, and with this characteristic, having an accurate diagnosis of its incidence is a problem that health personnel face every day. That is why having all the indispensable tools to achieve optimal results is of utmost importance. Time is an essential factor when identifying heart problems, specialists look for and develop options to improve this aspect, which requires a thorough analysis of the patient, electrocardiograms being the factor standard for diagnosis and monitoring of patients. In this paper, we review patents and combined systems for the analysis of existing electrocardiogram signals, specific to cardiovascular diseases. All these methods and equipment have the purpose of giving an accurate diagnosis and a prediction of the presence of CVD in patients with positive risk factors. These are considered as the first diagnostic option, based on the guidelines already established in the field of preventive cardiology. The methodology consists of the searching of specific electrocardiography and cardiovascular disease subjects, taking as a reference the use of various patent databases. A total of 2634 patents were obtained in the consulted databases. Of that total, only 30 patents that met all the previous criteria were considered; furthermore, a second in-depth review of their information was conducted. It is expected that studying and reviewing these patents will allow us to know the variety of tools available for the different pathologies that make up CVD, not only for its immediate diagnosis because, as mentioned, the time factor is decisive for the best forecast but also to allow us to follow up on all the cases that arise, being able to provide a better quality of life to patients with CVD or even being able to lead them to a full recovery. Full article
(This article belongs to the Section Algorithms and Mathematical Models for Computer-Assisted Diagnostic Systems)
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<p>WIPO classification for patents in the area of health and informatics.</p> Full article ">Figure 2
<p>Patent analysis flow chart.</p> Full article ">Figure 3
<p>Number of patents per country.</p> Full article ">
44 pages, 3503 KiB  
Article
Long-Term Visitation Value for Deep Exploration in Sparse-Reward Reinforcement Learning
by Simone Parisi, Davide Tateo, Maximilian Hensel, Carlo D’Eramo, Jan Peters and Joni Pajarinen
Algorithms 2022, 15(3), 81; https://doi.org/10.3390/a15030081 - 28 Feb 2022
Cited by 3 | Viewed by 3265
Abstract
Reinforcement learning with sparse rewards is still an open challenge. Classic methods rely on getting feedback via extrinsic rewards to train the agent, and in situations where this occurs very rarely the agent learns slowly or cannot learn at all. Similarly, if the [...] Read more.
Reinforcement learning with sparse rewards is still an open challenge. Classic methods rely on getting feedback via extrinsic rewards to train the agent, and in situations where this occurs very rarely the agent learns slowly or cannot learn at all. Similarly, if the agent receives also rewards that create suboptimal modes of the objective function, it will likely prematurely stop exploring. More recent methods add auxiliary intrinsic rewards to encourage exploration. However, auxiliary rewards lead to a non-stationary target for the Q-function. In this paper, we present a novel approach that (1) plans exploration actions far into the future by using a long-term visitation count, and (2) decouples exploration and exploitation by learning a separate function assessing the exploration value of the actions. Contrary to existing methods that use models of reward and dynamics, our approach is off-policy and model-free. We further propose new tabular environments for benchmarking exploration in reinforcement learning. Empirical results on classic and novel benchmarks show that the proposed approach outperforms existing methods in environments with sparse rewards, especially in the presence of rewards that create suboptimal modes of the objective function. Results also suggest that our approach scales gracefully with the size of the environment. Full article
(This article belongs to the Special Issue Reinforcement Learning Algorithms)
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<p>A simple problem where naive exploration performs poorly. The agent starts in the second leftmost cell and is rewarded only for finding a treasure. It can move up/down/left/right, but if it moves up or down its position resets. Acting randomly at each step takes on average <math display="inline"><semantics> <msup> <mn>4</mn> <mi>N</mi> </msup> </semantics></math> attempts to find the rightmost and most valuable reward, where <span class="html-italic">N</span> is the number of cells to the right of the agent. As no reward is given in any intermediate cell, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math>-greedy exploration is likely to converge to the local optimum represented by the leftmost reward if <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> decays too quickly.</p> Full article ">Figure 2
<p>Toy problem domain.</p> Full article ">Figure 3
<p><b>Toy example (part 1)</b>. Visitation count (<b>a</b>) and behavior policies (<b>b</b>–<b>d</b>) for the toy problem below. Cells are divided into four triangles, each one representing the count (<b>a</b>) or the behavior Q-value (<b>b</b>–<b>d</b>) for the actions “up/down/left/right” in that cell. Arrows denote the action with the highest Q-value. None of the behavior policies exhibits long-term deep exploration. In (1,3) both UCB1 (<b>c</b>) and the augmented Q-table (<b>d</b>) myopically select the action with the smallest immediate count. The latter also acts badly in (1,2) and (2,3). There, it selects “left” which has count one, instead of “up” which has count zero.</p> Full article ">Figure 4
<p><b>Toy example (part 2)</b>. Visitation count (<b>a</b>) and behavior policies derived from the proposed W-functions (<b>b</b>,<b>c</b>). Due to the low count, the exploration upper bound dominates the greedy Q-value, and the proposed behavior policies successfully achieve long-term exploration. Both policies prioritize unexecuted actions and avoid terminal and prison states.</p> Full article ">Figure 5
<p>Chainworld with uniform count.</p> Full article ">Figure 6
<p><b>Toy example (part 3)</b>. Behavior policies under uniform visitation count. In the top row, reward states (1,1) and (3,1) are terminal. In the bottom row, they are not and the MDP has an infinite horizon. All state-action pairs have been executed once, except for “left” in (1,3). Only the proposed methods (<b>d</b>,<b>e</b>) correctly identify such state-action pair as the most interesting for exploration and propagate this information to other states thanks to TD learning. When the action is executed, all policies converge to the greedy one (<b>a</b>).</p> Full article ">Figure 7
<p>The deep sea.</p> Full article ">Figure 8
<p><b>Results on the deep sea domain</b> averaged over 20 seeds. The proposed exploration achieves the best results, followed by bootstrapped exploration.</p> Full article ">Figure 9
<p>The taxi driver.</p> Full article ">Figure 10
<p><b>Results on the taxi</b> domain averaged over 20 seeds. The proposed algorithms outperform all others, being the only solving the task without optimistic initialization.</p> Full article ">Figure 11
<p>The deep gridworld.</p> Full article ">Figure 12
<p><b>Results on the deep gridworld</b> averaged over 20 seeds. Once again, the proposed algorithms are the only solving the task without optimistic initialization.</p> Full article ">Figure 13
<p>The “toy” gridworld.</p> Full article ">Figure 14
<p>The “prison” gridworld.</p> Full article ">Figure 15
<p>The “wall” gridworld.</p> Full article ">Figure 16
<p><b>Results on the toy gridworld</b> averaged over 20 seeds. Bootstrapped and bonus-based exploration perform well, but cannot match the proposed one (blue and orange line overlap).</p> Full article ">Figure 17
<p><b>The “prison” and distractors</b> affect the performance of all algorithms but ours.</p> Full article ">Figure 18
<p><b>The final gridworld</b> emphasizes the better performance of our algorithms.</p> Full article ">Figure 19
<p><b>Visitation count at the end of the learning.</b> The seed is the same across all images. Initial states naturally have a higher count than other states. Recall that the upper portion of the deep sea and some gridworlds cells cannot be visited. Only the proposed methods explore the environment uniformly (figures show the count of UCB-based W-function. Count-based W-function performed very similarly). Other algorithms myopically focus on distractors.</p> Full article ">Figure 20
<p><b>Performance of the our algorithms on varying of</b><math display="inline"><semantics> <msub> <mi>γ</mi> <mi>w</mi> </msub> </semantics></math> on the “toy” gridworld (<a href="#algorithms-15-00081-f014" class="html-fig">Figure 14</a>). The higher <math display="inline"><semantics> <msub> <mi>γ</mi> <mi>w</mi> </msub> </semantics></math>, the more the agent explores, allowing to discover the reward faster.</p> Full article ">Figure 21
<p><b>Visitation count for</b><math display="inline"><semantics> <msubsup> <mi>W</mi> <mi mathvariant="normal">N</mi> <mi>β</mi> </msubsup> </semantics></math><b>at the end of the learning</b> on the same random seed (out of 20). The higher the discount, the more uniform the count is. The initial state (bottom left) has naturally higher counts because the agent always starts there. <math display="inline"><semantics> <msubsup> <mi>W</mi> <mrow> <mi>UCB</mi> </mrow> <mi>β</mi> </msubsup> </semantics></math> performed very similarly.</p> Full article ">Figure 22
<p><b>Steps to learn on varying the deep sea size</b><math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>59</mn> </mrow> </semantics></math>, averaged over ten runs with 500,000 steps limit. For filled dots, the run always converged, and we report the 95% confidence interval with error bars. For empty dots connected with dashed lines, the algorithm did not learn within the step limit at least once. In this case, the average is over converged runs only and we do not report any confidence interval. Using the exploration bonus (pink) learning barely converged once (most of its dots are either missing or empty). Using bootstrapping (red) all runs converged, but the results show a large confidence interval. With random prior (green) the learning rarely did not converge, and performed very similarly across the random seeds, as shown by its extremely small confidence interval. On the contrary, our method (blue, orange) is the only always converging with a confidence interval close to zero. Indeed, it outperforms all baseline by attaining the lowest sample complexity. Missing algorithms (random, <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math>-greedy, UCB1, Thompson sampling) performed poorly and are not reported.</p> Full article ">Figure 23
<p>The ergodic chainworld.</p> Full article ">Figure 24
<p><b>Visitation counts for the chainworld</b> with 27 states (x-axis) over time (y-axis). As time passes (top to bottom), the visitation count grows. Only our algorithms and UCB1 explore uniformly, producing a uniform colormap. However, UCB1 finds the last state (with the reward) much later. Once UCB1 finds the reward ((<b>c</b>), step 1000) the visitation count increases only in the last state. This suggests that when UCB1 finds the reward contained in the last state it effectively stops exploring other states. By contrast, our algorithms keep exploring the environment for longer. This allows the agent to learn the true Q-function for all states and explains why our algorithms achieve lower sample complexity and MSVE.</p> Full article ">Figure 25
<p><b>Sample complexity on varying the chain size</b><math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>59</mn> </mrow> </semantics></math>. Error bars denote 95% confidence interval. Only the proposed algorithms (blue and orange lines almost overlap) show little sensitivity to <math display="inline"><semantics> <mi>ε</mi> </semantics></math>, as their sample complexity only slightly increases as <math display="inline"><semantics> <mi>ε</mi> </semantics></math> decreases. By contrast, other algorithms are highly influenced by <math display="inline"><semantics> <mi>ε</mi> </semantics></math>. Their estimate complexity has a large confidence interval, and for smaller <math display="inline"><semantics> <mi>ε</mi> </semantics></math> they rarely learn an <math display="inline"><semantics> <mi>ε</mi> </semantics></math>-optimal policy.</p> Full article ">Figure 26
<p><b>Sample complexity against <math display="inline"><semantics> <mi>ε</mi> </semantics></math>, and MSVE</b> over time for 27- and 55-state chainworlds. Shaded areas denote 95% confidence interval. As shown in <a href="#algorithms-15-00081-f025" class="html-fig">Figure 25</a>, the sample complexity of our approach is barely influenced by <math display="inline"><semantics> <mi>ε</mi> </semantics></math>. Even for <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, our algorithms attain low sample complexity, whereas other algorithms complexity is several orders of magnitude higher. Similarly, only our algorithms learn an almost perfect Q-function, achieving an MSVE close to zero.</p> Full article ">Figure 27
<p><b>Results with stochastic transition function</b> on three of the previous MDPs. Once again, only our algorithms visit all states and learn the optimal policy within steps limit in all MDPs, and their performance is barely affected by the stochasticity.</p> Full article ">Figure A1
<p>Comparison of the proposed exploration against <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math>-greedy and bootstrapped exploration with and without replay memory. Each line denotes the average over 20 seeds. Only exploration based on the visitation value always learns in both domains, i.e., both with and without local optima (distractor rewards), regardless of the memory.</p> Full article ">
17 pages, 976 KiB  
Article
Predicting Dynamic User–Item Interaction with Meta-Path Guided Recursive RNN
by Yi Liu, Chengyu Yin, Jingwei Li, Fang Wang and Senzhang Wang
Algorithms 2022, 15(3), 80; https://doi.org/10.3390/a15030080 - 28 Feb 2022
Cited by 1 | Viewed by 3485
Abstract
Accurately predicting user–item interactions is critically important in many real applications, including recommender systems and user behavior analysis in social networks. One major drawback of existing studies is that they generally directly analyze the sparse user–item interaction data without considering their semantic correlations [...] Read more.
Accurately predicting user–item interactions is critically important in many real applications, including recommender systems and user behavior analysis in social networks. One major drawback of existing studies is that they generally directly analyze the sparse user–item interaction data without considering their semantic correlations and the structural information hidden in the data. Another limitation is that existing approaches usually embed the users and items into the different embedding spaces in a static way, but ignore the dynamic characteristics of both users and items. In this paper, we propose to learn the dynamic embedding vector trajectories rather than the static embedding vectors for users and items simultaneously. A Metapath-guided Recursive RNN based Shift embedding method named MRRNN-S is proposed to learn the continuously evolving embeddings of users and items for more accurately predicting their future interactions. The proposed MRRNN-S is extended from our previous model RRNN-S which was proposed in the earlier work. Comparedwith RRNN-S, we add the word2vec module and the skip-gram-based meta-path module to better capture the rich auxiliary information from the user–item interaction data. Specifically, we first regard the interaction data of each user with items as sentence data to model their semantic and sequential information and construct the user–item interaction graph. Then we sample the instances of meta-paths to capture the heterogeneity and structural information from the user–item interaction graph. A recursive RNN is proposed to iteratively and mutually learn the dynamic user and item embeddings in the same latent space based on their historical interactions. Next, a shift embedding module is proposed to predict the future user embeddings. To predict which item a user will interact with, we output the item embedding instead of the pairwise interaction probability between users and items, which is much more efficient. Through extensive experiments on three real-world datasets, we demonstrate that MRRNN-S achieves superior performance by extensive comparison with state-of-the-art baseline models. Full article
(This article belongs to the Special Issue Graph Embedding Applications)
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<p>(<b>a</b>) Illustration of two user interaction sequences: Bob buys a cell phone, a phone case, a phone film, and a mobile earphone; Alice buys a suit, a dress, a shoe, and a hat, successively. (<b>b</b>) A toy example of an interaction network containing three users and four items. Each arrow represents an interaction from a user to an item. Each interaction is associated with a timestamp <span class="html-italic">t</span> and a feature vector <span class="html-italic">f</span> (such as the feature of the commodity).</p> Full article ">Figure 2
<p>The framework of the proposed MRRNN-S.</p> Full article ">Figure 3
<p>An illustration of the interaction sequence of a user with items.</p> Full article ">Figure 4
<p>(<b>a</b>) An example of user–item interaction graph. (<b>b</b>) An example of metapath.</p> Full article ">Figure 5
<p>The training loss curves of MRRNN-S over the three datasets.</p> Full article ">Figure 6
<p>The percentage of each variant’s performance to the performance of the full model on the two datasets.</p> Full article ">Figure 7
<p>The impact of different embedding dimensions on the JingDong dataset.</p> Full article ">Figure 8
<p>(<b>a</b>) Recall@K with different <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>I</mi> </msub> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>U</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) Recall@K with different <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>U</mi> </msub> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>I</mi> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>Percentage of training data.</p> Full article ">
20 pages, 21029 KiB  
Article
An Effective Algorithm for Finding Shortest Paths in Tubular Spaces
by Dang-Viet-Anh Nguyen, Jérôme Szewczyk and Kanty Rabenorosoa
Algorithms 2022, 15(3), 79; https://doi.org/10.3390/a15030079 - 25 Feb 2022
Cited by 1 | Viewed by 2949
Abstract
We propose a novel algorithm to determine the Euclidean shortest path (ESP) from a given point (source) to another point (destination) inside a tubular space. The method is based on the observation data of a virtual particle (VP) assumed to move along this [...] Read more.
We propose a novel algorithm to determine the Euclidean shortest path (ESP) from a given point (source) to another point (destination) inside a tubular space. The method is based on the observation data of a virtual particle (VP) assumed to move along this path. In the first step, the geometric properties of the shortest path inside the considered space are presented and proven. Utilizing these properties, the desired ESP can be segmented into three partitions depending on the visibility of the VP. Our algorithm will check which partition the VP belongs to and calculate the correct direction of its movement, and thus the shortest path will be traced. The proposed method is then compared to Dijkstra’s algorithm, considering different types of tubular spaces. In all cases, the solution provided by the proposed algorithm is smoother, shorter, and has a higher accuracy with a faster calculation speed than that obtained by Dijkstra’s method. Full article
(This article belongs to the Special Issue Network Science: Algorithms and Applications)
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<p>The regular and self-overlapping tube. The regular tube ensures the correctness of the directed graph in the following section.</p> Full article ">Figure 2
<p>Discrete approach for the ESP problem. (<b>Left</b>) Inner space of the tube transformed into a series of meshed circular disks; and (<b>Right</b>) the directed graph.</p> Full article ">Figure 3
<p>(<b>Left</b>) The dashed red rays describe the positive directions. (<b>Right</b>) <math display="inline"><semantics> <mi mathvariant="bold-italic">A</mi> </semantics></math> can see <math display="inline"><semantics> <mi mathvariant="bold-italic">B</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold-italic">D</mi> </semantics></math> because the line segments <math display="inline"><semantics> <mover> <mi mathvariant="bold-italic">AB</mi> <mo>¯</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mover> <mi mathvariant="bold-italic">AD</mi> <mo>¯</mo> </mover> </semantics></math> are totally contained by <math display="inline"><semantics> <mi mathvariant="sans-serif">Ω</mi> </semantics></math>. Furthermore, by this definition, <math display="inline"><semantics> <mi mathvariant="bold-italic">A</mi> </semantics></math> cannot see <math display="inline"><semantics> <mi mathvariant="bold-italic">C</mi> </semantics></math>. The green and blue dashed lines terminating at the boundary <math display="inline"><semantics> <mrow> <mo>∂</mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math> illustrate the line of sights. Among them, the blue one is the longest length of sight, an important concept used in the following method.</p> Full article ">Figure 4
<p>The visible area of a cross-section <math display="inline"><semantics> <msub> <mi>S</mi> <mi>i</mi> </msub> </semantics></math> is described by the yellow zone(s) which must be unique and continuous.</p> Full article ">Figure 5
<p>Curved segments lying on surfaces of positive and zero curvatures where A and B can see each other.</p> Full article ">Figure 6
<p>(<b>Left</b>) Tube portion between the cross-sections containing <math display="inline"><semantics> <mi mathvariant="bold-italic">X</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math> which can see each other. <math display="inline"><semantics> <mfenced open="(" close=")"> <mi>α</mi> </mfenced> </semantics></math> is an arbitrary plane containing <math display="inline"><semantics> <mi mathvariant="bold-italic">XY</mi> </semantics></math> but not containing <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>˙</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>. The ESP <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">p</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </semantics></math> only changes its direction <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>˙</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> on its geodesic segment(s). <span class="html-italic">S</span> is an arbitrary cross-section of the tube where the geodesic segment crosses. (<b>Right</b>) On the projection view plane that is perpendicular to <math display="inline"><semantics> <mfenced open="(" close=")"> <mi>α</mi> </mfenced> </semantics></math> (<math display="inline"><semantics> <mfenced open="(" close=")"> <mi>α</mi> </mfenced> </semantics></math> degenerates to a straight line), as <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>¨</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> points outside the envelope of <span class="html-italic">S</span>, it also points away from <math display="inline"><semantics> <mfenced open="(" close=")"> <mi>α</mi> </mfenced> </semantics></math>. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>˙</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> points away from <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </semantics></math>, by mathematical induction, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>˙</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> will point away from <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>∀</mo> <mi>s</mi> <mo>∈</mo> <mfenced separators="" open="[" close="]"> <msub> <mi>s</mi> <mi>X</mi> </msub> <mo>,</mo> <msub> <mi>s</mi> <mi>Y</mi> </msub> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Point <math display="inline"><semantics> <mi mathvariant="bold-italic">X</mi> </semantics></math> can see cross-section <span class="html-italic">S</span>. <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math> is the intersection of the direction of the ESP <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="bold-italic">p</mi> <mo>˙</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> and the plane containing <span class="html-italic">S</span>. In <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> and through <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math>, we draw an arbitrary straight line that intersects the visible area <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. Let <math display="inline"><semantics> <mi mathvariant="bold-italic">W</mi> </semantics></math> be the intersection point that is closest to <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math>. (<b>Left</b>) <math display="inline"><semantics> <mi mathvariant="bold-italic">W</mi> </semantics></math> is in the inner zone of <span class="html-italic">S</span>; (<b>Right</b>) <math display="inline"><semantics> <mi mathvariant="bold-italic">W</mi> </semantics></math> is on the boundary of <span class="html-italic">S</span>.</p> Full article ">Figure 8
<p>Three partitions of the shortest path correspond to three sections of the tube. At <math display="inline"><semantics> <mi mathvariant="bold-italic">A</mi> </semantics></math> belonging to <b>P3</b>, the VP cannot see the ending cross-section <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </semantics></math>. The correct direction corresponds to the longest length of sight. At <math display="inline"><semantics> <mi mathvariant="bold-italic">B</mi> </semantics></math> belonging to <b>P2</b>, <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </semantics></math> can see been, but not <math display="inline"><semantics> <mi mathvariant="fraktur">Q</mi> </semantics></math>. The correct direction is towards the visible point <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math> in <math display="inline"><semantics> <msub> <mi>S</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </semantics></math> so that the angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> between <math display="inline"><semantics> <mi mathvariant="bold-italic">BY</mi> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">B</mi> <mi mathvariant="fraktur">Q</mi> </mrow> </semantics></math> is the smallest one. At <math display="inline"><semantics> <mi mathvariant="bold-italic">C</mi> </semantics></math> in <b>P1</b>, the particle can see <math display="inline"><semantics> <mi mathvariant="fraktur">Q</mi> </semantics></math>. The correct direction is towards <math display="inline"><semantics> <mi mathvariant="fraktur">Q</mi> </semantics></math>.</p> Full article ">Figure 9
<p>The oriented drilling process: (1) <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">C</mi> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </semantics></math> can see <math display="inline"><semantics> <mi mathvariant="bold-italic">T</mi> </semantics></math> in section <math display="inline"><semantics> <msub> <mi>S</mi> <mi>j</mi> </msub> </semantics></math>, (2) expand the examined direction in the vicinity of <math display="inline"><semantics> <mi mathvariant="bold-italic">T</mi> </semantics></math> until seeing <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">T</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> </semantics></math> in section <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>&gt;</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, (3) update <math display="inline"><semantics> <mi mathvariant="bold-italic">T</mi> </semantics></math> by <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">T</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>S</mi> <mi>j</mi> </msub> </semantics></math> by <math display="inline"><semantics> <msub> <mi>S</mi> <mi>k</mi> </msub> </semantics></math> and repeat step 2 for the new <math display="inline"><semantics> <mi mathvariant="bold-italic">T</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>S</mi> <mi>j</mi> </msub> </semantics></math>, (4) repeat step 3, (5) the expanding process is over and we do not find any farther section <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>=</mo> <mo>∅</mo> </mrow> </semantics></math>, and we then compare all the length of sight passing through the visible area in <math display="inline"><semantics> <msub> <mi>S</mi> <mi>j</mi> </msub> </semantics></math> to obtain the direction corresponding to the longest length of sight, and (6) initialize the next correct point of the shortest path <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">C</mi> <mi>i</mi> </msub> </semantics></math> as the intersection point between the correct direction and cross-section <math display="inline"><semantics> <msub> <mi>S</mi> <mi>i</mi> </msub> </semantics></math>.</p> Full article ">Figure 10
<p>Tubular space with two curved segments in space. By <b>L.P</b>, and <b>T.P</b>, we denote the path length and the computation time for the solution obtained by the proposed method. Similarly, <b>L.D</b>, and <b>T.D</b> for Dijkstra’s algorithm. The exact solution is determined by using Dijkstra’s method with <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>ρ</mi> </msub> <mo>=</mo> <mn>144</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>θ</mi> </msub> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>Canal space with convex and variable cross-sections.</p> Full article ">Figure A1
<p><math display="inline"><semantics> <mi mathvariant="bold-italic">X</mi> </semantics></math> can see the ending cross-section. By defining the cone surface <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </semantics></math>, we can prove that <math display="inline"><semantics> <mi mathvariant="fraktur">Q</mi> </semantics></math> is coplanar with <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">X</mi> <mo>,</mo> <mi mathvariant="bold-italic">I</mi> <mo>,</mo> <mi mathvariant="bold-italic">Y</mi> </mrow> </semantics></math>.</p> Full article ">Figure A2
<p><math display="inline"><semantics> <mi mathvariant="bold-italic">X</mi> </semantics></math> cannot see the ending cross-section. It can only see one point <math display="inline"><semantics> <mi mathvariant="bold-italic">Y</mi> </semantics></math> on the farthest visible cross-section <math display="inline"><semantics> <msub> <mi>S</mi> <mi>f</mi> </msub> </semantics></math>.</p> Full article ">
37 pages, 1000 KiB  
Article
Deterministic Approximate EM Algorithm; Application to the Riemann Approximation EM and the Tempered EM
by Thomas Lartigue, Stanley Durrleman and Stéphanie Allassonnière
Algorithms 2022, 15(3), 78; https://doi.org/10.3390/a15030078 - 25 Feb 2022
Cited by 5 | Viewed by 3421
Abstract
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step has been replaced by Monte Carlo (MC), Markov Chain Monte [...] Read more.
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step has been replaced by Monte Carlo (MC), Markov Chain Monte Carlo or tempered approximations, etc. Most of the well-studied approximations belong to the stochastic class. By comparison, the literature is lacking when it comes to deterministic approximations. In this paper, we introduce a theoretical framework, with state-of-the-art convergence guarantees, for any deterministic approximation of the E step. We analyse theoretically and empirically several approximations that fit into this framework. First, for intractable E-steps, we introduce a deterministic version of MC-EM using Riemann sums. A straightforward method, not requiring any hyper-parameter fine-tuning, useful when the low dimensionality does not warrant a MC-EM. Then, we consider the tempered approximation, borrowed from the Simulated Annealing literature and used to escape local extrema. We prove that the tempered EM verifies the convergence guarantees for a wider range of temperature profiles than previously considered. We showcase empirically how new non-trivial profiles can more successfully escape adversarial initialisations. Finally, we combine the Riemann and tempered approximations into a method that accomplishes both their purposes. Full article
(This article belongs to the Special Issue Stochastic Algorithms and Their Applications)
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<p>(<b>a</b>) Average values, with standard deviation, over 2000 simulations of the negative log-likelihood along the steps of the Riemann EM. The Riemann EM increases the likelihood. (<b>b</b>) Average and standard deviation of the relative parameter reconstruction errors at the end of the Riemann EM.</p> Full article ">Figure 2
<p>(<b>a</b>) Visual representation of the number of Riemann intervals over the EM steps for each profile <math display="inline"><semantics> <msub> <mi>φ</mi> <mi>i</mi> </msub> </semantics></math>. The total number of Riemann intervals computed over 100 EM iterations are: 5150 for “low”, 14,950 for “medium”, 50,500 for “linear” and 104,950 for “high”. (<b>b</b>) For each profile, average evolution of the negative log-likelihood, with standard deviation, over 50 simulations. The results are fairly similar, in particular between “medium”, “high” and “linear”.</p> Full article ">Figure 3
<p>(<b>a</b>) Visual representation of the number of Riemann intervals over the EM steps for each profile <math display="inline"><semantics> <msub> <mi>φ</mi> <mi>i</mi> </msub> </semantics></math>. In higher dimension, the computational complexity of the profiles are very different. More precisely, the total number of Riemann squares computed over 100 EM iterations are: 4534 for “square root”, 125,662 for “5 square root”, 348,550 for “low” and 2,318,350 for “medium”. (<b>b</b>) For each profile, average evolution of the negative log-likelihood, with standard deviation, over 50 simulations. The “square root” profile performs poorly. However, the other three are comparable despite their different computational complexities.</p> Full article ">Figure 4
<p>500 sample points from a Mixture of Gaussians with 3 classes. The true centroid of each Gaussian are depicted by black crosses, and their true covariance matrices are represented by the confidence ellipses of level 0.8, 0.99 and 0.999 around the centre. Each sub-figure corresponds to one of the three different versions of the true parameters. From (<b>a</b>) to (<b>c</b>): the true <math display="inline"><semantics> <msub> <mi>μ</mi> <mi>k</mi> </msub> </semantics></math> of the two left clusters (<math display="inline"><semantics> <msub> <mi>μ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>μ</mi> <mn>2</mn> </msub> </semantics></math>) are getting closer while everything else stays identical.</p> Full article ">Figure 5
<p>Typical final positioning of the centroids by EM (first row) and tmp-EM with <span class="html-italic">oscillating</span> profile (second row) <b>when the initialisation is made at the barycenter of all data points</b> (blue crosses). The three columns represent the three gradually more ambiguous parameter sets. Each figure represents the positions of the estimated centroids after convergence of the EM algorithms (orange cross), with their estimated covariance matrices (orange confidence ellipses). In each simulation, 500 sample points were drawn from the real GMM (small green crosses). In those example, tmp-EM managed to correctly identify the position of the three real centroids.</p> Full article ">Figure 6
<p>Typical final positioning of the centroids by EM (first row) and tmp-EM with <span class="html-italic">oscillating</span> profile (second row) <b>when the initialisation is made by selecting two points in the isolated cluster and one in the lower ambiguous cluster</b> (blue crosses). The three columns represent the three gradually more ambiguous parameter sets. Each figure represents the positions of the estimated centroids after convergence of the EM algorithms (orange cross), with their estimated covariance matrices (orange confidence ellipses). In each simulation, 500 sample points were drawn from the real GMM (small green crosses). In those examples, although EM kept two centroids on the isolated cluster, tmp-EM managed to correctly identify the position of the three real centroids.</p> Full article ">Figure 7
<p>Results over many simulations of the Riemann EM and tmp-Riemann EM on the Beta-Gaussian model. The tempered Riemann EM reaches relative errors on the real parameters that are orders of magnitude below the Riemann EM with no temperature. The likelihood reached is also lower with the tempering.</p> Full article ">
16 pages, 4605 KiB  
Article
Prediction of Injuries in CrossFit Training: A Machine Learning Perspective
by Serafeim Moustakidis, Athanasios Siouras, Konstantinos Vassis, Ioannis Misiris, Elpiniki Papageorgiou and Dimitrios Tsaopoulos
Algorithms 2022, 15(3), 77; https://doi.org/10.3390/a15030077 - 24 Feb 2022
Cited by 8 | Viewed by 4478
Abstract
CrossFit has gained recognition and interest among physically active populations being one of the most popular and rapidly growing exercise regimens worldwide. Due to the intense and repetitive nature of CrossFit, concerns have been raised over the potential injury risks that are associated [...] Read more.
CrossFit has gained recognition and interest among physically active populations being one of the most popular and rapidly growing exercise regimens worldwide. Due to the intense and repetitive nature of CrossFit, concerns have been raised over the potential injury risks that are associated with its training including rhabdomyolysis and musculoskeletal injuries. However, identification of risk factors for predicting injuries in CrossFit athletes has been limited by the absence of relevant big epidemiological studies. The main purpose of this paper is the identification of risk factors and the development of machine learning-based models using ensemble learning that can predict CrossFit injuries. To accomplish the aforementioned targets, a survey-based epidemiological study was conducted in Greece to collect data on musculoskeletal injuries in CrossFit practitioners. A Machine Learning (ML) pipeline was then implemented that involved data pre-processing, feature selection and well-known ML models. The performance of the proposed ML models was assessed using a comprehensive cross validation mechanism whereas a discussion on the nature of the selected features is also provided. An area under the curve (AUC) of 77.93% was achieved by the best ML model using ensemble learning (Adaboost) on the group of six selected risk factors. The effectiveness of the proposed approach was evaluated in a comparative analysis with respect to numerous performance metrics including accuracy, sensitivity, specificity, AUC and confusion matrices to confirm its clinical relevance. The results are the basis for the development of reliable tools for the prediction of injuries in CrossFit. Full article
(This article belongs to the Special Issue Ensemble Algorithms and/or Explainability)
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<p>Accuracy with respect to the number of selected features for all the competing algorithms.</p> Full article ">Figure 2
<p>Confusion matrixes of the six competing ML models: (<b>a</b>) SVM, (<b>b</b>) LR, (<b>c</b>) DT, (<b>d</b>) KNN, (<b>e</b>) Adaboost and (<b>f</b>) RF.</p> Full article ">Figure 3
<p>(<b>a</b>) Receiver–operating characteristic curves, (<b>b</b>) Precision–recall curves for ML models.</p> Full article ">Figure 3 Cont.
<p>(<b>a</b>) Receiver–operating characteristic curves, (<b>b</b>) Precision–recall curves for ML models.</p> Full article ">Figure 4
<p>Reliability diagrams of the competing ML models.</p> Full article ">
35 pages, 3759 KiB  
Article
Partitioning of Transportation Networks by Efficient Evolutionary Clustering and Density Peaks
by Pamela Al Alam, Joseph Constantin, Ibtissam Constantin and Clelia Lopez
Algorithms 2022, 15(3), 76; https://doi.org/10.3390/a15030076 - 24 Feb 2022
Cited by 2 | Viewed by 3193
Abstract
Road traffic congestion has became a major problem in most countries because it affects sustainable mobility. Partitioning a transport network into homogeneous areas can be very useful for monitoring traffic as congestion is spatially correlated in adjacent roads, and it propagates at different [...] Read more.
Road traffic congestion has became a major problem in most countries because it affects sustainable mobility. Partitioning a transport network into homogeneous areas can be very useful for monitoring traffic as congestion is spatially correlated in adjacent roads, and it propagates at different speeds as a function of time. Spectral clustering has been successfully applied for the partitioning of transportation networks based on the spatial characteristics of congestion at a specific time. However, this type of classification is not suitable for data that change over time. Evolutionary spectral clustering represents a state-of-the-art algorithm for grouping objects evolving over time. However, the disadvantages of this algorithm are the cubic time complexity and the high memory demand, which make it insufficient to handle a large number of data sets. In this paper, we propose an efficient evolutionary spectral clustering algorithm that solves the drawbacks of evolutionary spectral clustering by reducing the size of the eigenvalue problem. This algorithm is applied in a dynamic environment to partition a transportation network into connected homogeneous regions that evolve with time. The number of clusters is selected automatically by using a density peak algorithm adopted for the classification of traffic congestion based on the sparse snake similarity matrix. Experiments on the real network of Amsterdam city demonstrate the superiority of the proposed algorithm in robustness and effectiveness. Full article
(This article belongs to the Special Issue Nature-Inspired Algorithms in Machine Learning)
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<p>A data flow chart describing our methodological steps.</p> Full article ">Figure 2
<p>The two graph models are explained using two different examples. (<b>a</b>) The primal graph model, which consists of representing the intersections by nodes and the roads by edges. (<b>b</b>) The dual graph model, which consists of considering the roads as the graph nodes and the crossing point between them as edges.</p> Full article ">Figure 3
<p>Example of a snake initialized by a link in red. The green links represent the neighborhood, according to a 2D approach (<b>a</b>) and a 3D approach (<b>b</b>) [<a href="#B24-algorithms-15-00076" class="html-bibr">24</a>].</p> Full article ">Figure 4
<p>Variance of two snakes of the graph of links.</p> Full article ">Figure 5
<p>Snake computed on the network of the sixth district of Paris. The number of links in the snake is equal to 64.</p> Full article ">Figure 6
<p>Two graphs at time periods <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> and <span class="html-italic">t</span>.</p> Full article ">Figure 7
<p>Amsterdam reduced network with 208 roads [<a href="#B24-algorithms-15-00076" class="html-bibr">24</a>].</p> Full article ">Figure 8
<p>The mean values of connected clusters’ dissimilarity versus snake length computed as a percentage of the size of the network of roads.</p> Full article ">Figure 9
<p>The mean values of connected clusters’ dissimilarity versus the weight coefficient <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>.</p> Full article ">Figure 10
<p>Decision graph for the time period <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math> using the density peak algorithm and the probability density function.</p> Full article ">Figure 11
<p>Clustering results for the time period <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math> in the case of the density peak (<b>a</b>), modularity (<b>b</b>) and eigengap (<b>c</b>).</p> Full article ">Figure 12
<p>Histogram of link speeds for the time period = 6 in the case of the density peak.</p> Full article ">Figure 13
<p>Histogram of link speeds for the time period = 6 in the case of the modularity.</p> Full article ">Figure 14
<p>Histogram of link speeds for the time period = 6 in the case of the eigengap.</p> Full article ">Figure 15
<p>The number of clusters obtained by applying the density peak, the modularity and the eigengap methods for each time period.</p> Full article ">Figure 16
<p>Variation of the total cost for the PCQ framework using the density peak, the modularity and the eigengap methods. The total cost function is defined as a linear combination of the snapshot cost (SC) and the temporal cost (TC).</p> Full article ">Figure 17
<p>Variation of the total cost for each time period in the case of time period = 10 min.</p> Full article ">Figure 18
<p>Comparing the average runtimes of the Evolutionary Spectral Clustering (ESC) and the Efficient Evolutionary Spectral Clustering (EESC) algorithms for PCQ and PCM frameworks.</p> Full article ">Figure 19
<p>Clustering results for time periods from <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> for the IND, PCM and PCQ methods in the case of time period = 10 min.</p> Full article ">Figure 20
<p>The mean values of connected clusters’ dissimilarity versus snake length computed in the percentage of the size of the network of roads in the case of time period = 20 min.</p> Full article ">Figure 21
<p>The mean values of connected clusters’ dissimilarity versus the weight coefficient <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> in the case of time period = 20 min.</p> Full article ">Figure 22
<p>The number of clusters obtained by applying the density peak method for each time period in the case of time period = 20 min.</p> Full article ">Figure 23
<p>Clustering results for time periods from <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> for the IND, PCM and PCQ methods in the case of time period = 20 min.</p> Full article ">Figure 24
<p>Clustering results for time periods from <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> for the IND, PCM and PCQ methods in the case of a time period equal to one hour.</p> Full article ">
19 pages, 5851 KiB  
Review
Machine Learning in Cereal Crops Disease Detection: A Review
by Fraol Gelana Waldamichael, Taye Girma Debelee, Friedhelm Schwenker, Yehualashet Megersa Ayano and Samuel Rahimeto Kebede
Algorithms 2022, 15(3), 75; https://doi.org/10.3390/a15030075 - 24 Feb 2022
Cited by 28 | Viewed by 8459
Abstract
Cereals are an important and major source of the human diet. They constitute more than two-thirds of the world’s food source and cover more than 56% of the world’s cultivatable land. These important sources of food are affected by a variety of damaging [...] Read more.
Cereals are an important and major source of the human diet. They constitute more than two-thirds of the world’s food source and cover more than 56% of the world’s cultivatable land. These important sources of food are affected by a variety of damaging diseases, causing significant loss in annual production. In this regard, detection of diseases at an early stage and quantification of the severity has acquired the urgent attention of researchers worldwide. One emerging and popular approach for this task is the utilization of machine learning techniques. In this work, we have identified the most common and damaging diseases affecting cereal crop production, and we also reviewed 45 works performed on the detection and classification of various diseases that occur on six cereal crops within the past five years. In addition, we identified and summarised numerous publicly available datasets for each cereal crop, which the lack thereof we identified as the main challenges faced for researching the application of machine learning in cereal crop detection. In this survey, we identified deep convolutional neural networks trained on hyperspectral data as the most effective approach for early detection of diseases and transfer learning as the most commonly used and yielding the best result training method. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications III)
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<p>Flow chart for hyper-spectral image data analysis and processing for wheat rust detection [<a href="#B58-algorithms-15-00075" class="html-bibr">58</a>].</p> Full article ">Figure 2
<p>UAV system and photo-bike used for hyperspectral imaging of wheat farms [<a href="#B61-algorithms-15-00075" class="html-bibr">61</a>].</p> Full article ">Figure 3
<p>Deep Convolutional Neural Network architecture for the detection of rice blast [<a href="#B65-algorithms-15-00075" class="html-bibr">65</a>].</p> Full article ">Figure 4
<p>Distribution of research papers by year.</p> Full article ">Figure 5
<p>Distribution of machine learning techniques.</p> Full article ">
18 pages, 4363 KiB  
Article
Machine Learning-Based Monitoring of DC-DC Converters in Photovoltaic Applications
by Marco Bindi, Fabio Corti, Igor Aizenberg, Francesco Grasso, Gabriele Maria Lozito, Antonio Luchetta, Maria Cristina Piccirilli and Alberto Reatti
Algorithms 2022, 15(3), 74; https://doi.org/10.3390/a15030074 - 23 Feb 2022
Cited by 29 | Viewed by 5134
Abstract
In this paper, a monitoring method for DC-DC converters in photovoltaic applications is presented. The primary goal is to prevent catastrophic failures by detecting malfunctioning conditions during the operation of the electrical system. The proposed prognostic procedure is based on machine learning techniques [...] Read more.
In this paper, a monitoring method for DC-DC converters in photovoltaic applications is presented. The primary goal is to prevent catastrophic failures by detecting malfunctioning conditions during the operation of the electrical system. The proposed prognostic procedure is based on machine learning techniques and focuses on the variations of passive components with respect to their nominal range. A theoretical study is proposed to choose the best measurements for the prognostic analysis and adapt the monitoring method to a photovoltaic system. In order to facilitate this study, a graphical assessment of testability is presented, and the effects of the variable solar irradiance on the selected measurements are also considered from a graphical point of view. The main technique presented in this paper to identify the malfunction conditions is based on a Multilayer neural network with Multi-Valued Neurons. The performances of this classifier applied on a Zeta converter are compared to those of a Support Vector Machine algorithm. The simulations carried out in the Simulink environment show a classification rate higher than 90%, and this means that the monitoring method allows the identification of problems in the initial phases, thus guaranteeing the possibility to change the work set-up and organize maintenance operations for DC-DC converters. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fault Detection and Diagnosis)
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<p>Voltage–Current curves of the photovoltaic panel; (<b>a</b>) curves obtained with fixed temperature (25 °C) as the irradiance varies, (<b>b</b>) curves obtained with fixed irradiance (1000 W/m<sup>2</sup>) as the temperature varies.</p> Full article ">Figure 2
<p>General diagram of the photovoltaic system and Zeta converter circuit.</p> Full article ">Figure 3
<p>Converter currents in time domain: (<b>a</b>) current <span class="html-italic">I<sub>L</sub></span><sub>1</sub>; (<b>b</b>) current in the inductor <span class="html-italic">I<sub>L</sub></span><sub>2</sub>.</p> Full article ">Figure 4
<p>General configuration of the MLMVN and error definition in the output layer.</p> Full article ">Figure 5
<p>Set-up of the output layer and coding of the classes.</p> Full article ">Figure 6
<p>Variations of the working point and variations of the input current and voltage.</p> Full article ">Figure 7
<p>Sensitivity of the measurements with respect to the variation of environmental conditions; (<b>a</b>) ripple of the voltage on the first capacitor <span class="html-italic">V<sub>C1ripple</sub></span>; (<b>b</b>) ripple of the voltage on the second capacitor <span class="html-italic">V<sub>C2ripple</sub></span>; (<b>c</b>) mean value of the current through the first inductor <span class="html-italic">I<sub>L1mean</sub></span>; (<b>d</b>) mean value of the current through the second inductor <span class="html-italic">I<sub>L2mean</sub></span>.</p> Full article ">Figure 7 Cont.
<p>Sensitivity of the measurements with respect to the variation of environmental conditions; (<b>a</b>) ripple of the voltage on the first capacitor <span class="html-italic">V<sub>C1ripple</sub></span>; (<b>b</b>) ripple of the voltage on the second capacitor <span class="html-italic">V<sub>C2ripple</sub></span>; (<b>c</b>) mean value of the current through the first inductor <span class="html-italic">I<sub>L1mean</sub></span>; (<b>d</b>) mean value of the current through the second inductor <span class="html-italic">I<sub>L2mean</sub></span>.</p> Full article ">Figure 8
<p>Testability analysis of the Zeta converter through SapWin and TAPSLIN.</p> Full article ">Figure 9
<p>Classification Results; (<b>a</b>) performance of the classifier during the training phase: the red line represents the CR of the learning phase, and the blue line is the CR obtained in the test phase; (<b>b</b>) classification results for each fault class shown in the Matlab application at the end of each training epoch.</p> Full article ">Figure 10
<p>Comparison between MLMVN and SVM; (<b>a</b>) performance obtained by processing measurements under the same conditions of the training phase; (<b>b</b>) performance obtained by processing measurements with different irradiance and temperature values.</p> Full article ">Figure 11
<p>Classification rate with respect to the number of neurons in the hidden layer.</p> Full article ">
13 pages, 271 KiB  
Article
Reinforcement Learning for Mean-Field Game
by Mridul Agarwal, Vaneet Aggarwal, Arnob Ghosh and Nilay Tiwari
Algorithms 2022, 15(3), 73; https://doi.org/10.3390/a15030073 - 22 Feb 2022
Cited by 4 | Viewed by 2841
Abstract
Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously. After taking an action, the state of every agent updates to the next state, and each agent receives a [...] Read more.
Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously. After taking an action, the state of every agent updates to the next state, and each agent receives a reward. However, finding an equilibrium (if exists) in this game is often difficult when the number of agents becomes large. This paper focuses on finding a mean-field equilibrium (MFE) in an action-coupled stochastic game setting in an episodic framework. It is assumed that an agent can approximate the impact of the other agents’ by the empirical distribution of the mean of the actions. All agents know the action distribution and employ lower-myopic best response dynamics to choose the optimal oblivious strategy. This paper proposes a posterior sampling-based approach for reinforcement learning in the mean-field game, where each agent samples a transition probability from the previous transitions. We show that the policy and action distributions converge to the optimal oblivious strategy and the limiting distribution, respectively, which constitute an MFE. Full article
(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)
15 pages, 4052 KiB  
Article
A Machine Learning Approach for Solving the Frozen User Cold-Start Problem in Personalized Mobile Advertising Systems
by Iosif Viktoratos and Athanasios Tsadiras
Algorithms 2022, 15(3), 72; https://doi.org/10.3390/a15030072 - 22 Feb 2022
Cited by 7 | Viewed by 3116
Abstract
A domain that has gained popularity in the past few years is personalized advertisement. Researchers and developers collect user contextual attributes (e.g., location, time, history, etc.) and apply state-of-the-art algorithms to present relevant ads. A problem occurs when the user has limited or [...] Read more.
A domain that has gained popularity in the past few years is personalized advertisement. Researchers and developers collect user contextual attributes (e.g., location, time, history, etc.) and apply state-of-the-art algorithms to present relevant ads. A problem occurs when the user has limited or no data available and, therefore, the algorithms cannot work well. This situation is widely referred in the literature as the ‘cold-start’ case. The aim of this manuscript is to explore this problem and present a prediction approach for personalized mobile advertising systems that addresses the cold-start, and especially the frozen user case, when a user has no data at all. The approach consists of three steps: (a) identify existing datasets and use specific attributes that could be gathered from a frozen user, (b) train and test machine learning models in the existing datasets and predict click-through rate, and (c) the development phase and the usage in a system. Full article
(This article belongs to the Section Evolutionary Algorithms and Machine Learning)
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<p>AUC scores for models regarding Avazu and Digix dataset.</p> Full article ">Figure 2
<p>Log-loss scores for models regarding Avazu and Digix dataset.</p> Full article ">Figure 3
<p>AUC scores for the balanced undersampled Avazu and Digix datasets.</p> Full article ">Figure 4
<p>Log-loss scores for the balanced undersampled Avazu and Digix datasets.</p> Full article ">Figure 5
<p>Implementation–development step.</p> Full article ">
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