Abstract
In modern society, the scientific symbiotic relationship of aesthetic community space is crucial for the development of cities. This article aimed to explore the symbiotic relationship between aesthetic community space and science, and analyze this relationship based on the k-means clustering algorithm. The article analyzed the spatial characteristics of different types of aesthetic communities, as well as the commonalities and differences between aesthetic communities and science, including the complementary relationship between the two. The k-means clustering algorithm is integrated to classify community spatial features, thereby analyzing and optimizing the relationship between the two. The experiment selected a sample of an aesthetic community and divided it into three different types of spatial features: architectural area, landscape greening area, and other activity areas. This article also compared the clustering results of the k-means algorithm with the k-means algorithm based on three-dimensional grid space. The results showed that the k-means algorithm optimized by the principle of three-dimensional grid space had stronger clustering performance. In the experiment, four different types of clustering algorithms and multiple evaluation indicators were also selected for testing. The data showed that in the clustering of spatial features in building areas, the k-means average clustering error score was controlled at around 13–14 under different missing ratios; the minimum average clustering error score of the characteristic data of the landscape greening area was 12.1. The average clustering error score in spatial feature clustering of other activity areas reached a minimum value of 23.5 when the missing ratio was 10%, which was lower than other algorithms. The overall experimental results indicate that the fused k-means clustering algorithm can effectively partition the aesthetic community space and optimize scientific symbiotic relationships.
1 Introduction
With the popularization of social media and the Internet, aesthetic communities have gradually become an important platform for people to showcase their personal aesthetic views and share artistic works. The interaction and exchange in this community environment have played a positive role in promoting aesthetic creation and artistic development. Space science, as an interdisciplinary research field, explores the interaction between humans and the environment. As a social network constructed in a specific spatial environment, the operation and spatial layout of aesthetic communities play an important role in the development and influence of aesthetics. However, there are still certain difficulties in studying the spatial layout of aesthetic communities and the symbiotic relationship between science and art. Computational aesthetics is a bridge between science and art and is becoming a new interdisciplinary field [1]. The k-means clustering algorithm is a common unsupervised learning algorithm, which can divide data samples into different clusters. In the research of aesthetic community spatial science, the k-means algorithm can be used to cluster and analyze the attributes and interaction behaviors of community members, thereby revealing the symbiotic relationships and interaction patterns within the community [2].
The symbiosis of aesthetic community space and science is a complex social phenomenon, involving a variety of factors and variables. In recent years, multiple scholars have studied the relationship between the two, providing certain research results for the fields of spatial planning and aesthetics. For example, in the field of public space aesthetics research, Caymaz Gokcen Firdevs Yucel examined and analyzed the advanced aesthetics, functionality, and environmental performance of urban public spaces by evaluating the current status of urban public spaces and highlighting the role of creativity in developing these spaces [3]. He used analytical description methods to obtain a set of results to determine the realistic results of the aesthetic, functional, and environmental performance of urban public spaces [4]. In spatial planning, Rahbar utilized a data-driven generation approach to generate comprehensive spatial distribution probabilities. The resulting floor plan can play a role in the initial stage of architectural design [5]. Regarding aesthetic environmental design, Pow explored the governance logic and planning epistemology in the transformation of China’s framework ecological civilization plan, and depicted the outline of China’s emerging aesthetic urban system. This system gradually incorporates aesthetic standards into governance practices and urban planning as a normative approach to managing urban growth in China and promoting a sustainable urban future [6]. In view of the effectiveness of the environmental design of the public meeting space, McLane applied social science-based research methods and spatial analysis to understand how to improve specific internal space, which is the key to the recovery process. He stated that the success of residential gathering spaces that promote and support residents’ relationships and reduce user marginalization is influenced by a series of social space design factors, as well as facility policies and activity planning [7]. Based on historical and cultural research on urban design, planning, and politics, Laage-Thomsen implemented a sustainable agricultural park project led by citizens in Copenhagen. He provided a new imaginative space for the public’s aesthetic standards and analyzed it, thus solving the contradiction faced when intervening and evaluating the diverse green space structure of cities [8]. According to the emotional reactions of residents caused by the community environment, Chen suggested that when planning and creating a happy community, material and perceptual environments should be considered. When the impact on the physical environment and service functionality is similar, the contextual impact dominates. These findings provide important new insights that urban and architectural professionals can use to create communities that are more livable and attractive to their residents [9]. These documents have certain reference significance for the study of the relationship between the spatial characteristics of aesthetic communities and scientific symbiosis.
Clustering algorithms can divide datasets into different categories based on certain similarity measures, thus accurately analyzing the features in aesthetic community spaces [10]. In recent years, they have gradually become a research hotspot in the field of spatial planning and design. For example, Kim proposed a reliable method for urban structural planning, mainly based on clustering analysis, using new similarity measures to reveal urban structure [11]. This study combines repeated spectral clustering and hierarchical clustering to obtain a reliable structure that maintains the continuity of clustering and determines the hierarchical structure of different regional units [8]. In addition, in large-scale spatial planning, Vysochan divided Ukraine’s regions based on its tourism development level and used k-means and k-means++ techniques for attribute clustering analysis to solve tourism planning problems [12]. In order to cluster data that are not linearly separable in the original feature space, Yao introduced multiple kernel learning in k-means clustering to obtain the optimal kernel combination for clustering. He developed an effective optimization method to reduce the time complexity of optimizing core combination weights. Extensive experiments on benchmark and real world data sets have proved the effectiveness and superiority of the proposed method [13]. These literatures have certain research value in analyzing the symbiotic relationship of aesthetic community space science, but they have not been analyzed in conjunction with the current situation [14].
This article explored the symbiotic relationship of aesthetic community spatial science by integrating k-means clustering algorithm [15]. By applying the k-means clustering algorithm and taking the aesthetic community space as the research object, this article explored the scientific symbiotic relationship within it. It would collect relevant data on the aesthetic community space and preprocess it to ensure the accuracy and availability of the data. This article provided a detailed introduction to the principle and application of k-means clustering algorithm and analyzed its advantages in the study of symbiotic relationships in aesthetic community spatial science. After summarizing and analyzing the research results, it reveals the importance and value of integrating k-means clustering algorithm into aesthetic community spatial scientific symbiosis relationships.
2 Model on the symbiotic relationship between aesthetic community space and science
2.1 Characteristics of aesthetic community space
Aesthetic community space refers to the collective shared space with aesthetics as the core value in the community environment [16]. It is a concept that combines aesthetic theory with community development, aiming to provide a place for collective creation and appreciation of art and aesthetics. It creates an aesthetic perception and emotional resonance through the display of artworks, the beautification, and the construction of the environment. This space has a unique design and layout, allowing people to feel the power of beauty and artistic charm within it. People can establish relationships and interactions with each other by participating in various artistic activities, cultural exchanges, and creative output. The spatial characteristics of aesthetic communities have certain characteristics, including spatial layout, decorative elements, green landscapes, facilities, and equipment.
2.1.1 Spatial layout
The layout of aesthetic community space should conform to the characteristics of human visual, auditory, and psychological perception, and follow human behavioral habits and social patterns. The visual appearance of the architectural space environment reflects the values of residents, and the practice of architectural environment needs to consider aesthetics [17]. Therefore, the layout of the aesthetic community space is reasonable, orderly, and layered, which can guide people to streamline and create a sense of pleasure in the space.
Inclusive public spaces are representative of responsive, democratic, and meaningful spaces in the context of urban development [18]. The spatial layout features include spatial scale and proportion, which are important factors affecting the visual effect of space. The aesthetic community space takes into account people’s sense of scale and proportion, and different scales of space can create different atmospheres and experiences. The form and structure of the second space, the form of the aesthetic community space, takes into account aesthetic principles such as the sense of hierarchy, symmetry, and axis of the space. The reasonable layout of the spatial structure increases the functionality and aesthetics of the space. The color and material of the third space are important elements in the design of aesthetic community spaces. The choice of color includes the function of space, atmosphere, and people’s psychological feelings. In addition, lighting design is an indispensable factor in aesthetic community space design, which not only affects the brightness and brightness of the space but also creates different emotions and atmospheres. Light design includes the use of natural and artificial light, as well as factors such as the direction and angle of light exposure.
The community space layout in Figure 1 achieves spatial scale and proportion, also considers spatial form and structure, and can demonstrate the role of light in the community space. The color combination is also quite beautiful. The space of an aesthetic community usually focuses on the beauty of the design layout. Architectural design would focus on the coordination of overall style and proportion, while interior design would focus on the beauty of color matching and furniture placement. According to the functions and activity needs of the community, the space can be reasonably divided. For example, community activity venues, leisure areas, learning areas, creative areas, etc., can be divided into different areas to meet the needs of different activities
2.1.2 Decorative elements
Analyzing and extracting decorative elements can help designers and artists better understand and apply aesthetic community space decoration elements, thereby creating works with more artistic value and aesthetic sense. The characteristics of aesthetic community space decoration elements include the following aspects:
Color characteristics refer to the analysis of the colors used in spatial decorative elements, including main tones, auxiliary colors, and color matching methods. Color is one of the most intuitive and obvious features of spatial decorative elements. Colors can be reflected through various means such as walls, furniture, and fabric. Different colors have different emotions and effects, and can be used to create different atmospheres.
Texture features are the textures used to analyze spatial decorative elements, including the type of material, texture, and feel. Material refers to the texture and touch of decorative elements. Different materials can bring different feelings and experiences to people. For example, smooth glass material can give people a sense of modernity and coldness, while wooden material can give people a sense of nature and warmth.
Shape features analyze the shape of spatial decorative elements, including the curvature of lines, the size of angles, and the simplicity and complexity of shapes. The shape features of elements can be extracted through mathematical methods such as geometric shapes and curves.
The proportional feature is the analysis of the proportional relationship between spatial decorative elements, including the comparison of size, the proportion of height, and the proportion of space. The proportional features of elements can be extracted through measurement and calculation.
Patterns refer to the shapes, patterns, and textures of decorative elements. Different patterns can add interest and individuality to the space, such as patterns, geometric patterns, animal patterns, etc. The selection of patterns needs to consider the overall effect and spatial style. Shape refers to the shape and outline of decorative elements. Different shapes can bring different changes and effects to space, for example, a circle can give a soft feeling, while a square can give a stable and upright feeling.
In summary, the characteristics of aesthetic community space decoration elements can be classified and extracted through colors, materials, patterns, and shapes. Through intelligent image processing and analysis techniques, image features can be effectively extracted and classified for decorative elements in space, such as colors, textures, etc.
2.1.3 Greening landscape
Greening landscapes can enhance the aesthetic and attractiveness of community spaces. The landscape of green trees and blooming flowers can add natural landscape elements to the community, creating a pleasant living environment. The green landscape of aesthetic community space plays an important role in improving living quality, improving the environment, promoting social interaction, and has a positive impact on the development of residents and communities. It can promote sustainable development of community environment, and sustainable benefits can be estimated in terms of urban biodiversity conservation and aesthetic green urban space [19]. The landscape characteristics of aesthetic community space greening can be divided into the following categories:
Plant characteristics include the type and quantity of plants, their morphology, color, and texture. The selection of plants should focus on aesthetics, seasonal changes, and diversity.
The spatial layout characteristics refer to the layout and organizational form of green landscapes in a community. For example, a reasonable division of green landscape space can be designed, including courtyards, flower beds, lawns, and walkways, as well as their relationships and connections.
Structural features refer to the infrastructure, landscape elements, and decorations in green landscapes. For example, fountains, sculptures, and horticultural structures, can be set up to enhance the sense of hierarchy and artistry of the landscape.
Material characteristics refer to the types and textures of materials used in green landscapes. For example, natural materials such as wood, stone, cement, etc., or artificial materials such as synthetic lawns, plastic flower pots, and so on, can be used to create different appearances and styles.
Functional characteristics refer to the functions and uses of green landscapes, such as providing leisure and entertainment spaces, sports venues, and social gathering points. These functions should be coordinated with the overall style and aesthetic tone of the green landscape.
2.1.4 Facilities and equipment
Aesthetic community spaces typically include various types of facilities and equipment to meet the needs of different groups of people. The facilities and equipment in the aesthetic community space comply with the principles of environmental protection and sustainable development. The facilities and equipment of the aesthetic community space have the characteristics of diversification, high quality, sustainability, humanized design, and innovation, so as to provide residents with a rich and colorful activity experience. The characteristics of facilities and equipment in the aesthetic community space can be divided into the following categories:
Building facilities include the main buildings in the community, such as residential buildings, commercial buildings, public facilities, etc. These buildings should have a good exterior design, conform to the overall aesthetic style, and provide a comfortable living and usage environment.
Public space facilities include facilities in public spaces such as parks, squares, and leisure areas, such as benches, rest booths, amusement facilities, etc. These facilities should comply with ergonomic principles, provide a convenient and comfortable user experience, and be harmonious and unified with the surrounding environment.
Transportation facilities include facilities in traffic spaces such as roads, sidewalks, and bicycle lanes; traffic signs; street lights; pedestrian trees. These facilities should not only meet the requirements of traffic safety and convenience but also be coordinated with the surrounding environment while emphasizing aesthetic design and landscape integration.
Lighting facilities include outdoor lighting and landscape lighting equipment, such as street lights, landscape lights, and courtyard lights. The selection and layout of lighting facilities should consider lighting effects, energy conservation, and environmental protection, and be coordinated with surrounding buildings and landscapes.
The above-analyzed features can be used as data sources for the spatial clustering of aesthetic communities. Through spatial feature clustering analysis, the distribution and commonalities of spatial features of aesthetic communities can be understood, providing reference and guidance for scientific design and planning of aesthetic communities. In practical operation, clustering algorithms can be used to cluster aesthetic communities based on the similarity of features. The clustering results can be displayed visually. At the same time, it is possible to further analyze the similarities and differences in the spatial features of aesthetic communities by comparing the characteristics of different categories.
2.2 Cluster analysis of the symbiotic relationship between community space and science
2.2.1 Symbiotic relationship
The relationship between aesthetic community space and science can be understood as interdependent and mutually reinforcing. Aesthetic community space refers to a community environment and architectural space created and shaped by humans, with certain aesthetic value and artistic value. Science, on the other hand, explains the laws and principles of objective things in a rational way through observation, experimentation, and reasoning. The symbiosis between aesthetic community space and science has the following aspects:
The creation of aesthetic community space relies on scientific knowledge: the design and construction of aesthetic community space cannot be separated from the research and application of scientific principles such as materials, structure, spatial layout, etc. Science provides technology and methods to enable the aesthetic community space to better realize people’s aesthetic and functional requirements.
Science can be validated and applied through aesthetic community spaces: the results of scientific research can be validated through practical applications in aesthetic community spaces. For example, scientific research has shown that greening the environment has a positive impact on people’s psychological and physical health, so appropriate greening elements can be added when designing aesthetic community spaces.
Aesthetic community space can provide places and conditions for scientific research: scientific research requires a series of scientific facilities and conditions such as laboratories and workplaces, and aesthetic community space can provide these places. For example, art galleries, libraries, and other places in aesthetic community spaces can serve as places for scientific research and learning.
The maintenance of aesthetic community space requires scientific support: the maintenance and management of aesthetic community space also requires scientific support. Science can provide relevant technology and knowledge to better protect and repair aesthetic community spaces, extending their lifespan.
There is a certain relationship between aesthetic community space and scientific symbiosis, but research on this relationship is currently relatively limited. Therefore, this article will use clustering algorithms to explore the symbiotic relationship between aesthetic community space and science, and construct a clustering analysis model for the symbiotic relationship between community space and science. The symbiotic relationship between aesthetic community space and science can be quantified and cluster analyzed, and visualized. The model would be constructed below.
2.2.2 Sample selection
For the relevant data on the study of aesthetic community space and scientific symbiosis relationship, it uses the characteristics of aesthetic community space analyzed previously as the basis for research and observes the layout design, landscape, decoration style, and other characteristics of aesthetic community space on site. It records whether scientific elements are incorporated, such as scientific laboratories, scientific books, etc. This article takes a sample of aesthetic community space designed in a city in Sichuan Province, China, to study and analyze the relationship between community space and scientific symbiosis. It analyzes the spatial layout and appearance features, quantifies and classifies features through spatial clustering methods, and explores the relationship between the two.
Based on this sample, this article collects data on relevant community spaces. Figure 1 shows the floor plan of community space planning:
Community space sample plan division.
After selecting samples, this article selects appropriate features based on the research questions of the space and scientific formulas to be analyzed. It can choose features such as the size, color, style, and materials of the community space as inputs.
2.2.3 Data standardization
The standardization of aesthetic community spatial data refers to the transformation of original data into data that are close to the standard normal distribution with a mean of 0 and a standard deviation of 1. The commonly used standardization is the standard score method. Its principle is to make the transformed data meet the characteristics of standard normal distribution through linear transformation of the original data and calculate the mean and standard deviation of each index. Each data point is standardized as follows:
In formula (1), z represents the standardized data, and X represents the original data;
2.2.4 Feature extraction
In the study of the symbiotic relationship between aesthetic community space and science, feature extraction of aesthetic community space is an important task. This article selects the k-means clustering algorithm for feature extraction and analysis. The k-means algorithm is a clustering algorithm that can divide a set of data into k clusters, each with a representative center point. Clustering is an exploratory data analysis technique used to study the underlying structure of data [20]. An aesthetic community can be seen as a collection of images generated by a group of users, and each image can be represented as a feature vector that contains the spatial features of the image. In the extraction of aesthetic community spatial features based on the k-means algorithm, it first needs to select a suitable set of spatial features to represent each image. These features can be combined into a feature vector as input data. One of the most significant issues in cluster analysis is determining the number of clusters in unlabeled data, which is an input to most clustering algorithms [21]. The feature extraction of aesthetic community space based on the k-means algorithm mainly involves dividing the dataset into k clusters, so that each data point belongs to the closest cluster to it, thereby achieving feature extraction and clustering analysis. The distance calculation formula of the k-means algorithm usually calculates the distance between data points and cluster centers through Euclidean distance:
In formula (2), x and y represent the coordinates of the data point and cluster center, respectively. The k-means algorithm cluster center calculation formula uses the average value of data points in each cluster as the new cluster center:
In formula (3), C represents the new cluster center; N represents the number of data points in the cluster;
For the clustering of aesthetic community spatial features, the center of the clustering is usually located in areas with high density, which is easily surrounded by other low-density feature points. Therefore, the denser the data points around the aesthetic community spatial data sample, the easier it is to become the clustering center, thus enabling accurate clustering analysis. Therefore, the spatial distribution of aesthetic community is very important for clustering analysis. Therefore, the principle of local analysis can be used to improve the k-means algorithm. By calculating the local density and determining the possible relationship to become the cluster center, the local mapping is calculated using the following formula:
In formula (4), x represents the data sample points;
2.3 k-means clustering based on three-dimensional grid space
Due to the fact that the aesthetic community space is three-dimensional, in order to perform clustering analysis on it, it is necessary to understand the design of three-dimensional grid spaces. The three-dimensional grid space is based on the theory of two-dimensional space, which refers to the three-dimensional coordinate system. Space can be divided into small cubic units, each of which is called a grid. The sample set of aesthetic community space can be mapped to three-dimensional space, assuming that the sample set is X = {
In formula (5), attributes x, y, and z all represent the feature dimension, and the segmentation step size d of the dimension can be expressed as
In formula (6),
Clustering iteration diagram of three-dimensional grid space.
Through the study of the k-means algorithm, the relationship between aesthetic communities and scientific symbiosis can be explored, revealing their interaction and influence. The relevant data of aesthetic community space and scientific symbiosis can be used as input, and the k-means algorithm can be used for clustering analysis to analyze data in different clusters. This article compares their characteristics and attributes, understands their interaction and influence, and discovers the common features, similarities, and differences between aesthetic community space and scientific symbiosis. Below is an example analysis.
3 Fusion of k-means clustering algorithm for spatial feature data and evaluation
3.1 Community spatial feature clustering
To further evaluate the clustering effect of the k-means algorithm, this article conducts feature clustering tests on the selected aesthetic community spatial samples (Figure 3). It collects spatial data from aesthetic communities, including characteristic data of spatial elements such as buildings and green landscapes, such as size, shape, color, etc. Based on the experimental objectives, this article selects appropriate features for analysis and selects the shape and color of buildings as features for this experiment. Then, it uses the k-means algorithm to build a clustering model and selects the appropriate k-value, that is, the number of clusters. The clustering results can be visualized, and the spatial distribution of each category can be displayed using a two-dimensional scatter plot. This experiment tested the clustering effect of the k-means algorithm and the k-means clustering effect based on a three-dimensional grid structure. The test results are shown in Figure 3:
The clustering effect of the k-means algorithm on community space. (a) Clustering effect of k-means algorithm. (b) Clustering effect of k-means algorithm based on three-dimensional grid space.
Figure 3 shows the clustering effect based on three-dimensional grid space k-means and traditional k-means algorithms. From the clustering results of Figure 3a and b, it can be seen that the k-means algorithm based on three-dimensional grid space has a stronger clustering effect, while the traditional k-means algorithm has a more dispersed clustering effect. It can be seen that the k-means clustering algorithm based on three-dimensional grid space clusters sample points more closely, resulting in better clustering performance. This indicates that the k-means clustering algorithm based on three-dimensional grid space has certain clustering advantages.
By conducting experiments with different numbers of clusters and comparing their results and performance indicators, an appropriate number of clusters can be found to best characterize the characteristics of the community space. By applying different algorithms to the same community spatial dataset and comparing their clustering results, it can be determined which algorithm performs best in the task. This article uses subspace clustering error scores to evaluate the performance of various clustering algorithms, and the error score expression is as follows:
In formula (7), r is the number of misclassified samples, and
The performance of this algorithm in handling community spatial feature tasks can be improved. This article takes the latest subspace clustering algorithms based on Spectral clusterings, such as local subspace affinity (LSA), spectral curvature clustering (SCC), low-rank representation (LRR), sparse subspace clustering (SSC), and low-rank subspace clustering, as references. Table 1 shows the setting of experimental parameters:
Experimental parameter settings
| Experimental parameters | Set up |
|---|---|
| Central processing unit | 3.4 GHZ |
| Memory | 4 GB |
| Operating system | 64-bit Windows 10 |
| Experimental tools | MATLAB Ｒ2023a |
3.2 Experimental results
The experiment would divide the selected community samples into three types of characteristic data: building areas, landscaping areas, and other activity areas. It sets different missing rates on these three types of feature datasets, with missing rates set at 5, 10, 15, and 20%. Setting the missing ratio increases the rationality of the experiment and weakens the uncertainty caused by randomly generated missing data. This article runs k-means, LSA, SCC, LRR, and SSC algorithms to compare their clustering performance and perform clustering analysis on three different types of community spatial features. The evaluation indicators include average clustering error score, number of iterations, and four external evaluation indicators. This article conducted 10 experiments to take the mean and record the results as follows:
From the data results in Tables 2–4, it can be seen that the average clustering error score of the algorithm varies under different missing rates, and the average clustering error score also varies for different community spatial feature regions. First, the average clustering error score of the characteristic data of the building area was controlled at around 13–14 for the k-means average clustering error score under different missing ratios. The minimum average clustering error score was 13.1 when the missing ratio was 15%, while other algorithms included LSA, SCC, LRR, and SSC. When the missing ratio was 15%, the average clustering error score reaches the minimum value, which was 15.1, 17.2, 15.8, and 16.8 respectively, all of which were greater than the k-means algorithm. The second was the average clustering error score of the characteristic data of the landscape greening area, with the minimum k-means average clustering error score of 12.1. The minimum average clustering error scores of other algorithms LSA, SCC, LRR, and SSC for landscape green area feature data were 13.2, 13.4, 15.3, and 15.3, respectively. Several algorithms achieved their minimum values when the missing ratio was 5% and, finally, the average clustering error score of other active area feature data. The data shows that the k-means average clustering error score reached the minimum value of 23.5 when the missing ratio was 10%. Based on the above experimental data, it can be analyzed that the k-means algorithm can better analyze the feature types of community space, with fewer errors in clustering results and more accurate clustering results.
Comparison of average clustering error scores for characteristic data of building areas
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 15.3 | 17.5 | 16.3 | 17.3 | 13.2 |
| 10 | 15.3 | 17.2 | 16.2 | 16.8 | 13.5 |
| 15 | 15.1 | 17.2 | 15.8 | 16.8 | 13.1 |
| 20 | 16.1 | 17.3 | 16.9 | 17.2 | 14.1 |
Comparison of average clustering error scores for characteristic data of landscape greening areas
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 13.2 | 13.4 | 15.3 | 15.3 | 12.1 |
| 10 | 14.7 | 15.9 | 15.4 | 16.2 | 12.8 |
| 15 | 14.6 | 16.5 | 18.7 | 17.8 | 12.6 |
| 20 | 17.4 | 17.9 | 18.5 | 19.4 | 12.3 |
Comparison of average clustering error scores for feature data in other activity areas
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 29.4 | 29.5 | 28.5 | 32.8 | 25.4 |
| 10 | 30.5 | 31.9 | 29.4 | 33.7 | 23.5 |
| 15 | 31.5 | 31.3 | 27.4 | 34.5 | 26.7 |
| 20 | 35.8 | 33.4 | 30.2 | 32.9 | 30.3 |
According to the data in Tables 5–7, the average number of iterations of the algorithm varies under different missing values. Overall, the average number of iterations based on the k-means algorithm is relatively stable, indicating its strong convergence and stability. Other algorithms also have relatively stable average iterations. Here is the change chart of the Iterated function of the k-means algorithm in three community space features, as shown in Figures 4–6:
Comparison of average iterations of building area feature data sets
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 26 | 26 | 31 | 28 | 27 |
| 10 | 29 | 27 | 35 | 28 | 28 |
| 15 | 27 | 28 | 34 | 29 | 27 |
| 20 | 28 | 28 | 35 | 30 | 26 |
Comparison of average iterations of landscape greening area feature datasets
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 17 | 16 | 17 | 16 | 15 |
| 10 | 17 | 17 | 17 | 19 | 15 |
| 15 | 16 | 17 | 20 | 17 | 15 |
| 20 | 18 | 19 | 22 | 19 | 15 |
Comparison of average iteration times for feature datasets of other activity areas
| Missing ratio (%) | LSA | SCC | LRR | SSC | k-means |
|---|---|---|---|---|---|
| 5 | 35 | 37 | 38 | 38 | 39 |
| 10 | 37 | 38 | 40 | 39 | 38 |
| 15 | 39 | 36 | 48 | 40 | 36 |
| 20 | 40 | 37 | 50 | 43 | 38 |
Iterated function change diagram of k-means algorithm in spatial characteristics of building area.
Iterated function change of k-means algorithm in spatial characteristics of landscape greening area.
Iterated function change diagram of k-means algorithm in other active areas.
Figures 4–6 show the changes in the Iterated function of the k-means algorithm in different types of aesthetic community spatial feature clustering. From the data of function changes, it can be seen that the k-means algorithm can achieve convergence under different spatial feature types after clustering iteration, and the speed is fast. It can be seen that the Iterated function of the k-means algorithm can converge under different missing ratios, run smoothly, and have a good convergence effect.
Based on the selected evaluation indicators and through simulation testing, the clustering effects between different algorithms were obtained [22]. The evaluation indicator RI is a commonly used external evaluation indicator used to measure the consistency between clustering results and real category labels. The range of values for RI is [0,1]. The closer the value to 1, the higher the consistency between the clustering results and the real category labels, while the closer the value to 0, the lower the consistency. The higher the value of RI, the better. ARI is an indicator used to evaluate the performance of clustering algorithms, which is a modification of RI by considering the expected values in random situations to eliminate the impact of randomness. The value range of ARI is between −1 and 1, and the closer it is to 1, the more similar the clustering results are to the actual classification results. The closer to 0, the more random the clustering results are compared to the actual classification results. The closer it is to −1, the less similar the clustering results are to the actual classification results. The higher the value of ARI, the better. The range of JC coefficient values is between 0 and 1, and a larger value indicates a higher similarity between the two clustering results, indicating better clustering performance of the algorithm. MM is an indicator used to calculate the distance between two vectors, used to measure the degree of difference between two samples. The smaller the value of MM, the closer the distance between the two samples, that is the higher the similarity. Figures show the test results of these 5 algorithms, including LSA, SCC, LRR, SSC, and k-means algorithms. This article tests the performance of four different indicators under different missing ratios, including 5, 10, 15, and 20% missing ratios.
Figure 7 shows the test results of the spatial features of the building area in the sample of aesthetic community spatial features. From the test results, it can be seen that when the missing ratio was 5%, the RI, ARI, and JC indicators of the k-means algorithm were all the highest, with values of 0.834, 0.617, and 0.603. The MM indicator value was also small, with a values of 0.734. The minimum MM value of SSC was 0.732. When the missing ratio was 10%, the RI and JC values of the k-means algorithm were the highest, with values of 0.827 and 0.614. The highest value of the ARI evaluation index was LSA algorithm, which was 0.618. The MM value of the k-means algorithm reached a minimum of 0.710. When the missing ratio was 15%, the ARI and JC values of k-means were the highest, with values of 0.621 and 0.602. The RI value of the SSC algorithm reached its maximum of 0.824. The SSC algorithm also had the smallest MM value, with a value of 0.716. When the missing ratio was 20%, the k-means algorithm achieved the best performance among all evaluation indicators, with RI, ARI, and JC indicators having the highest values. The MM index value was also the smallest, with values of 0.828, 0.628, 0.606, and 0.714, respectively. Overall, the k-means algorithm performs the best in evaluating the clustering effect of spatial features in building areas.
Evaluation of clustering performance of community spatial features in different algorithms for building areas.
Figure 8 shows the evaluation results of the landscape greening area. According to the results, when the missing ratio was set to 5%, the k-means algorithm performed best among all evaluation indicators. The RI, ARI, and JC indicators all reached the highest values, with values of 0.824, 0.628, and 0.727, respectively. The MM evaluation value reached the lowest, with a value of 0.574. When the missing ratio was set to 10%, the k-means algorithm also performed the best, with the highest RI, ARI, and JC indicators of 0.82, 0.634, and 0.728. The MM indicator value was the smallest, at 0.575. When the missing ratio was set to 15%, the k-means algorithm had the highest RI and ARI index values, which were 0.823 and 0.649, respectively. The highest JC index value was the SSC algorithm, which was 0.729. The best performance of the MM indicator was also the k-means algorithm, with a value of 0.570. When the final missing proportion was 20%, the k-means algorithm performed the best in RI and JC indicators, with values of 0.827 and 0.738, respectively. The RI value of SSC was the same as that of the k-means algorithm, which was 0.827. The k-means algorithm had the best performance in MM evaluation, with a minimum value of 0.564. Overall, the k-means algorithm has the strongest clustering effect on community spatial features in landscape green areas.
Performance evaluation of community spatial feature clustering in landscape greening areas using different algorithms.
From the overall evaluation data above, it can be seen that the k-means algorithm has achieved significant results in clustering different types of spatial features in aesthetic communities. Compared with other clustering algorithms, the k-means algorithm can more accurately classify community spatial features. Through community spatial feature clustering, different aesthetic community spaces can be divided into different categories or groups. This can identify aesthetic community spaces with similar features and characteristics, and further explore their symbiotic relationship with science. Through horizontal comparison and longitudinal study of aesthetic community space with good clustering effect, such as the k-means algorithm, through aesthetic space feature clustering, it can understand the impact of different design elements and functional configurations on scientific symbiosis. This can optimize and improve the planning and design of aesthetic community spaces, enhancing their symbiotic effect with science.
4 Conclusions
This article focused on the symbiotic relationship between aesthetic community space and science, studied the classification of aesthetic community space characteristics, and analyzed the symbiotic relationship between aesthetic community and science. It built an aesthetic community spatial feature model based on a clustering algorithm and proposed a method to optimize the model based on the k-means clustering algorithm. By using the principle of three-dimensional grid space to optimize the k-means clustering model, it is applied to the classification of aesthetic community spatial features. A certain community space is selected as a sample and divided into different spatial areas, including building areas, landscape greening areas, and other activity areas. The experiment compared the experimental results of the k-means algorithm with other clustering algorithms and tested the values of evaluation indicators such as RI, ARI, JC, MM, etc. The results show that the k-means algorithm has better clustering performance, and experiments have verified the effectiveness and accuracy of the k-means method. k-means spatial feature clustering can be used to classify different aesthetic community spaces into different categories or groups. This article understands the characteristics and needs of different aesthetic community spaces and can provide targeted strategies and support for scientific symbiosis. This can further enhance the interaction and cooperation between aesthetic community space and science, and explore the opportunities and potential for scientific symbiosis in aesthetic community space.
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Funding information: This study did not receive any funding in any form.
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Author contributions: Y. Y. B. was responsible for the manuscript writing, research framework design, mode creation, and data analysis. Q. Q. Y. was responsible for the cording and liaising as part of the research project, organization research data, proofreading language, and processing images. All authors have read and agreed to the published version of the manuscript.
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Conflict of interest: The author(s) declare(s) that there is no conflict of interest regarding the publication of this article.
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Data availability statement: The data used to support the findings of this study are available from the corresponding author upon request.
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