Manifold Learning

卞云瀚
2023-12-01

http://www.math.ucla.edu/~wittman/mani/

 

Copied from lawhiu@cse.msu.edu.

Papers

ISOMAP and related

LLE and related

  • H. Chang, D.Y. Yeung, Y. Xiong. Super-resolution through neighbor embedding.Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), vol.1, pp.275-282, Washington, DC, USA, 27 June - 2 July 2004. (PDF)
  • D. de Ridder and M. Loog and M.J.T. Reinders. Local Fisher embedding. Proc. 17th International Conference on Pattern Recognition (ICPR2004), 2004.
  • L. K. Saul and S. T. Roweis. Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds.
    Journal of Machine Learning Research, v4, pp. 119-155, 2003.
  • Zhenyue Zhang and Hongyuan Zha. Local Linear Smoothing for Nonlinear Manifold Learning . CSE-03-003, Technical Report, CSE, Penn State Univ., 2003.
  • de Ritter D, Kouropteva O, Okun O, Pietikäinen M & Duin RPW.Supervised locally linear embedding.Artificial Neural Networks and Neural Information Processing, ICANN/ICONIP 2003 Proceedings, Lecture Notes in Computer Science 2714, Springer, 333-341.
  • Kouropteva O, Okun O & Pietikäinen M (2003) Classification of handwritten digits using supervised locally linear embedding algorithm and support vector machine. Proc. of the 11th European Symposium on Artificial Neural Networks (ESANN'2003), April 23-25, Bruges, Belgium, 229-234. Full paper
  • Hadid A & Pietikäinen M (2003). Efficient locally linear embeddings of imperfect manifolds.Proc. Machine Learning and Data Mining in Pattern Recognition. Lecture Notes in Computer Science 2734, Springer, 188-201
  • Kouropteva O, Okun O, Hadid A, Soriano M, Marcos S & Pietikäinen M (2002) Beyond Locally Linear Embedding Algorithm. Technical Report MVG-01-2002, University of Oulu, Machine Vision Group, Information Processing Laboratory, 49 p. Full paper
  • D. De Ridder and Duin, R.P.W. Locally linear embedding for classification, Technical report PH-2002-01, Pattern Recognition Group, Dept. of Imaging Science & Technology, Delft University of Technology, pp. 1-15, 2002.
  • Kouropteva O, Okun O & Pietikäinen M (2002) Selection of the optimal parameter value for the locally linear embedding algorithm. Proc. of the 1 st  International Conference on Fuzzy Systems and Knowledge Discovery (FSKD'02), November 18-22, Singapore, 359-363. Full paper
  • P. Perona and M. Polito. Grouping and dimensionality reduction by locally linear embedding. Neural Information Processing Systems 14 (NIPS'2001).
  • D. DeCoste. Visualizing Mercer Kernel Feature Spaces Via Kernelized Locally-Linear Embeddings.The 8th International Conference on Neural Information Processing(ICONIP2001), November 2001.
  • S. T. Roweis and L. K. Saul. Nonlinear Dimensionality Reduction by Locally Linear Embedding . Science, vol. 290, pp. 2323--2326, 2000.

Laplacian Eigenmap and other related

See also graph spectral methods.

Principal curves

Note: The site by K¨¦gl is probably a better resource on principal curves.

  • B. K¨¦gl , A. Krzyzak. Piecewise linear skeletonization using principal curves.IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 1, pp. 59-74, 2002.PDF ( Java implementation )
  • B. K¨¦gl, A. Krzyzak, T. Linder, K. Zeger. Learning and design of principal curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 3, pp. 281-297, 2000.IEEE Xplore
  • R. Tibshirani. Principal curves revisited. Statistics and Computing , vol 2, pp. 183--190, 1992
  • T. Hastie and W. Stuetzle. Principal curves. Journal of the American Statistical Association, vol 84, pp. 502--516, 1989
  • J.J. Verbeek, N. Vlassis, B. Krose A soft k-Segments Algorithm for Principal Curves . Proc. Int. Conf. on Artificial Neural Networks, 2001.
  • A. Smola, R. C. Williamson, S. Mika, and B. Scholkopf. Regularized principal manifolds . In Computational Learning Theory: 4th European Conference, volume 1572 of Lecture Notes in Artificial Intelligence, pages 214 -- 229. Springer, 1999.

Charting/co-ordination

Common issues

Estimating intrinsic dimensionality

SOM and related

Miscellaneous methods

Others

Applications

Presentation

Lecture on manifold learning by Roweis

http://www-leibniz.imag.fr/JournApprenSlides/HighDim.pdf

"Isomap: a global geometric framework for nonlinear dimensionality reduction"by Vin de Silva

NIPS workshop talk by Carrie Grimes

ISOMAP & Image articulation by Carrie Grimes

Global Geometric Framework for Nonlinear Dimensionality Reduction: The Isomap and Locally Linear Embedding Algorithm , presented by Kristin Branson

Computer examples (of ISOMAP)

Workshop of spectral methods in dimensionality reduction, clustering, and classification in NIPS 2002

Workshop website

  • Generative models implicit in spectral methods for manifold learning, by Vin de Silva and Joshua B. tenenbaum
  • Mathematical Foundations for Learning Image Manifolds Using ISOMAP and LLE, by Carrie Grimes and David Donoho (relatedurl )
  • The role of the Laplace-Beltrami Operator in Learning on Manifolds, by Mikhail Belkin and Partha Niyogi
  • Charting a manifold, by Matthew Brand
  • Automatic Alignment of Hidden Representations, by Yee Whye Teh and Sam T. Roweis
  • Convex Invariance Learning , by Tony Jebara
  • Laplacians, Spectra, and Kernels, by John Lafferty
  • Regularization for Continuous Data and Graphs, by Alex Smola
  • Generative Models of Affinity Matrices, by Romer Rosales and Brendan Frey
  • How Many Clusters? The Markov Random Walk Perspective, by Marina Meila
  • Also, Schoelkopf gave an improvised talk during the kernel workshop next day on the relationship between LLE and kernel PCA

Software

Some MDS matlab code

MDS site

http://www.math.ucla.edu/~wittman/mani/
Laplacian eigenmap software

VisuMap, a visualizer for high dimensional data (technical info) (paper)

Other resource page

Penn Dimensionality Reduction Reading Group

Dimensionality Reduction 

Manifold Learning

Acknowledgement

The following people have contributed to this page since 2005. I have also received help from other people before 2005, but I did not keep track of their names and thus I cannot express my gratitude here. Sorry!

  • Dr. Laskaris Nikos from Aristotle University of Thessaloniki

This page is (always!) under construction. Any suggestion is appreciated. Please reach me bylawhiu@cse.msu.edu .

 

 

http://www.cse.wustl.edu/~kilian/research/manifold/manifold.html

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