The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
A kernel view of the dimensionality reduction of manifolds
Open accessAbstract
We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.
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Cites
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
Nonlinear Component Analysis as a Kernel Eigenvalue Problem
Schölkopf, B., Smola, A., & Müller, K.-R. (1998) · Neural Computation · doi:10.1162/089976698300017467 · Cited by 8,084
Self-citationLaplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,621
Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering
Bengio, Y., Paiement, J.-F., Vincent, P., Delalleau, O., Roux, N. L., & Ouimet, M. (2003) · Cited by 894
Global Versus Local Methods in Nonlinear Dimensionality Reduction
de Silva, V., & Tenenbaum, J. B. (2002) · Cited by 787
Segmentation using eigenvectors: a unifying view
Weiss, Y. (1999) · Proceedings of the Seventh IEEE International Conference on Computer Vision · doi:10.1109/iccv.1999.790354 · Cited by 729
Diffusion Kernels on Graphs and Other Discrete Input Spaces
Kondor, R., & Lafferty, J. (2002) · Cited by 725
Diffusion kernels on graphs and other discrete structures
Kondor, R. (2002) · Cited by 449
Chung, F., & Yau, S.-T. (2000) · Journal of Combinatorial Theory, Series A · doi:10.1006/jcta.2000.3094 · Cited by 236
Cited by
Coifman, R. R., & Lafon, S. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.006 · Cited by 2,342
Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B., Warner, F., & Zucker, S. W. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0500334102 · Cited by 1,675
Foundations of Machine Learning
Mohri, M., Rostamizadeh, A., & Talwalkar, A. (2018) · doi:10.7551/mitpress/10290.001.0001 · Cited by 1,122
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
Nadler, B., Lafon, S., Coifman, R. R., & Kevrekidis, I. G. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2005.07.004 · Cited by 990
A Unifying Review of Deep and Shallow Anomaly Detection
Ruff, L., Kauffmann, J. R., Vandermeulen, R. A., Montavon, G., Samek, W., Kloft, M., Dietterich, T. G., & Muller, K.-R. (2021) · Proceedings of the IEEE · doi:10.1109/jproc.2021.3052449 · Cited by 914
Metadata
- Authors
- Ham, J., Lee, D. D., Mika, S., & Schölkopf, B.
- Venue
- Twenty-first international conference on Machine learning - ICML '04
- Publisher
- ACM Press
- Published
- 2004
- Pages
- 47
- OpenAlex
- W1966347620
- Cited by
- 532
- References
- 11
- Type
- conference abstract
- Language
- en
- Open access
- green
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