More Web Proxy on the site http://driver.im/

article

Incremental Laplacian eigenmaps by preserving adjacent information between data points

Authors:

Xinsheng Huang,

Dewen HuAuthors Info & Claims

Pattern Recognition Letters, Volume 30, Issue 16

Pages 1457 - 1463

https://doi.org/10.1016/j.patrec.2009.08.005

Published: 01 December 2009 Publication History

Abstract

Traditional nonlinear manifold learning methods have achieved great success in dimensionality reduction and feature extraction, most of which are batch modes. However, if new samples are observed, the batch methods need to be calculated repeatedly, which is computationally intensive, especially when the number or dimension of the input samples are large. This paper presents incremental learning algorithms for Laplacian eigenmaps, which computes the low-dimensional representation of data set by optimally preserving local neighborhood information in a certain sense. Sub-manifold analysis algorithm together with an alternative formulation of linear incremental method is proposed to learn the new samples incrementally. The locally linear reconstruction mechanism is introduced to update the existing samples' embedding results. The algorithms are easy to be implemented and the computation procedure is simple. Simulation results testify the efficiency and accuracy of the proposed algorithms.

References

[1]

The ISOMAP algorithm and topological stability. Science. v295. 7

[2]

Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE Trans. Pattern Anal. Machine Intell. v19 i7. 711-720.

[3]

Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. v15 i6. 1373-1396.

[4]

Adaptive Control Processes: A Guided Tour. Princeton University Press.

[5]

Out-of-sample extensions for LLE, ISOMAP, MDS, eigenmaps and spectral clustering. In: Advances in Neural Information Processing Systems, vol. 16. MIT Press.

[6]

Matrix Computations. third ed. The Johns Hopkins Univ. Press, Baltimore, MD.

[7]

Incremental locally linear embedding. Pattern Recognit. v38. 1764-1767.

[8]

Riemannian manifold learning. IEEE Trans. Pattern Anal. Machine Intell. v30 i5. 796-809.

[9]

Liu, X., Yin, J., Feng, Z., Dong, J., 2006. Incremental manifold learning via tangent space alignment. ANNPR 2006, LNAI 4087, pp. 107-121.

[10]

Incremental nonlinear dimensionality reduction by manifold learning. IEEE Trans. Pattern Anal. Machine Intell. v28 i3. 377-391.

[11]

Nonlinear dimensionality reduction by locally linear embedding. Science. v290. 2323-2326.

[12]

Skočaj, D., Leonardis, A., 2002. Weighted incremental subspace learning. In: Proceedings of Workshop on Cognitive Vision, Zurich.

[13]

Turk, M., Pentland, A.P., 1991. Face recognition using eigenfaces. In: IEEE Conf. on Computer Vision and Pattern Recognition.

[14]

Adaptive manifold learning. Proc. Adv. Neural Inform. Process. Systems. v17. 1473-1480.

[15]

Graph embedding and extensions: A general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Machine Intell. v29. 40-51.

[16]

IDR/QR: An incremental dimension reduction algorithm via QR decomposition. IEEE Trans. Knowl. Data Eng. v17. 1208-1222.

Digital Library

[17]

Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. v26 i1. 313-338.

Cited By

Xia JHuang LSun YDeng ZZhang XZhu M(2024)A Parallel Framework for Streaming Dimensionality ReductionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332651530:1(142-152)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326515
Madhavan SKumar N(2021)Incremental methods in face recognition: a surveyArtificial Intelligence Review10.1007/s10462-019-09734-354:1(253-303)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10462-019-09734-3
Kuleshov ABernstein A(2017)Nonlinear multi-output regression on unknown input manifoldAnnals of Mathematics and Artificial Intelligence10.1007/s10472-017-9551-081:1-2(209-240)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10472-017-9551-0
Show More Cited By

Incremental Laplacian eigenmaps by preserving adjacent information between data points
1. Computing methodologies

Recommendations

Local linear Laplacian eigenmaps

We have derived local linear Laplacian eigenmaps (LLLE) a manifold learning algorithm.The LLLE finds multiple local linear structures.The LLLE used P artificial neighbors to construct the adjacency graph.The experimental results indicate that it can ...
An improved incremental nonlinear dimensionality reduction for isometric data embedding

Manifold learning has become a hot issue in the field of machine learning and data mining. There are some algorithms proposed to extract the intrinsic characteristics of different type of high-dimensional data by performing nonlinear dimensionality ...
Soft adaptive loss based Laplacian eigenmaps
Abstract
The Laplacian eigenmaps (LE) is one of the most commonly used nonlinear dimensionality reduction methods and aims to find a low-dimensional representation to preserve the topological relationship between sample points in the original data. However,...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Pattern Recognition Letters

Pattern Recognition Letters Volume 30, Issue 16

December, 2009

83 pages

ISSN:0167-8655

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2009.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 December 2009

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Xia JHuang LSun YDeng ZZhang XZhu M(2024)A Parallel Framework for Streaming Dimensionality ReductionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332651530:1(142-152)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326515
Madhavan SKumar N(2021)Incremental methods in face recognition: a surveyArtificial Intelligence Review10.1007/s10462-019-09734-354:1(253-303)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10462-019-09734-3
Kuleshov ABernstein A(2017)Nonlinear multi-output regression on unknown input manifoldAnnals of Mathematics and Artificial Intelligence10.1007/s10472-017-9551-081:1-2(209-240)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10472-017-9551-0
Kreutzer PDotzler GRing MEskofier BPhilippsen MKim MRobbes RBird C(2016)Automatic clustering of code changesProceedings of the 13th International Conference on Mining Software Repositories10.1145/2901739.2901749(61-72)Online publication date: 14-May-2016
https://dl.acm.org/doi/10.1145/2901739.2901749
Malik ZHussain AWu J(2016)An online generalized eigenvalue version of Laplacian Eigenmaps for visual big dataNeurocomputing10.1016/j.neucom.2014.12.119173:P2(127-136)Online publication date: 15-Jan-2016
https://dl.acm.org/doi/10.1016/j.neucom.2014.12.119
Gao XLiang J(2015)An improved incremental nonlinear dimensionality reduction for isometric data embeddingInformation Processing Letters10.1016/j.ipl.2014.12.004115:4(492-501)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1016/j.ipl.2014.12.004
Raducanu BDornaika F(2014)Embedding new observations via sparse-coding for non-linear manifold learningPattern Recognition10.1016/j.patcog.2013.06.02147:1(480-492)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.patcog.2013.06.021
Orsenigo CVercellis C(2013)A comparative study of nonlinear manifold learning methods for cancer microarray data classificationExpert Systems with Applications: An International Journal10.1016/j.eswa.2012.10.04440:6(2189-2197)Online publication date: 1-May-2013
https://dl.acm.org/doi/10.1016/j.eswa.2012.10.044
Dornaika FAssoum ARaducanu B(2012)Automatic dimensionality estimation for manifold learning through optimal feature selectionProceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition10.1007/978-3-642-34166-3_63(575-583)Online publication date: 7-Nov-2012
https://dl.acm.org/doi/10.1007/978-3-642-34166-3_63
Raducanu BDornaika F(2012)Out-of-sample embedding by sparse representationProceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition10.1007/978-3-642-34166-3_37(336-344)Online publication date: 7-Nov-2012
https://dl.acm.org/doi/10.1007/978-3-642-34166-3_37

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents