The DOI matches its Crossref record; 41 of the 41 references it cites were found in a registry or an index.
Patch Alignment for Dimensionality Reduction
Abstract
Spectral analysis-based dimensionality reduction algorithms are important and have been popularly applied in data mining and computer vision applications. To date many algorithms have been developed, e.g., principal component analysis, locally linear embedding, Laplacian eigenmaps, and local tangent space alignment. All of these algorithms have been designed intuitively and pragmatically, i.e., on the basis of the experience and knowledge of experts for their own purposes. Therefore, it will be more informative to provide a systematic framework for understanding the common properties and intrinsic difference in different algorithms. In this paper, we propose such a framework, named "patch alignment,” which consists of two stages: part optimization and whole alignment. The framework reveals that 1) algorithms are intrinsically different in the patch optimization stage and 2) all algorithms share an almost identical whole alignment stage. As an application of this framework, we develop a new dimensionality reduction algorithm, termed Discriminative Locality Alignment (DLA), by imposing discriminative information in the part optimization stage. DLA can 1) attack the distribution nonlinearity of measurements; 2) preserve the discriminative ability; and 3) avoid the small-sample-size problem. Thorough empirical studies demonstrate the effectiveness of DLA compared with representative dimensionality reduction algorithms.
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(2012) · Encyclopedia of the Sciences of Learning · doi:10.1007/978-1-4419-1428-6_5195 · Cited by 19,370
THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS
FISHER, R. A. (1936) · Annals of Eugenics · doi:10.1111/j.1469-1809.1936.tb02137.x · Cited by 15,227
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Eigenfaces vs. Fisherfaces: recognition using class specific linear projection
Belhumeur, P. N., Hespanha, J. P., & Kriegman, D. J. (1997) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.598228 · Cited by 11,707
Analysis of a complex of statistical variables into principal components.
Hotelling, H. (1933) · Journal of Educational Psychology · doi:10.1037/h0071325 · Cited by 9,633
Goodall, C. (1988) · Technometrics · doi:10.1080/00401706.1988.10488412 · Cited by 8,675
Russell, E. L., Chiang, L. H., & Braatz, R. D. (2000) · Advances in Industrial Control · doi:10.1007/978-1-4471-0409-4_3 · Cited by 7,862
Chiang, L. H., Russell, E. L., & Braatz, R. D. (2001) · Advanced Textbooks in Control and Signal Processing · doi:10.1007/978-1-4471-0347-9_4 · Cited by 6,594
Face recognition using eigenfaces
Turk, M. A., & Pentland, A. P. (2002) · Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.1991.139758 · Cited by 5,197
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Metadata
- Authors
- Zhang, T., Tao, D., Li, X., & Yang, J.
- Venue
- IEEE Transactions on Knowledge and Data Engineering
- Published
- 2009-09
- Volume
- 21
- Issue
- 9
- Pages
- 1299-1313
- ISSN
- 1041-4347 (ISSN-L)
- OpenAlex
- W2132822263
- Cited by
- 381
- References
- 41
- FWCI
- 38.18
- Type
- journal article
- Language
- en
- Open access
- closed
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