Dimensionality Reduction Papers

(collected by Byron Yu)

Papers looking across multiple techniques
Isomap
Locally linear embedding (LLE)
Laplacian eigenmaps
Hessian LLE
Maximum variance unfolding
Conformal eigenmaps
Manifold alignment
Spectral graph theory tutorials
More papers

Papers looking across multiple techniques

Spectral methods for dimensionality reduction
L. K. Saul, K. Q. Weinberger, J. H. Ham, F. Sha, and D. D. Lee
In O. Chapelle, B. Schoelkopf, and A. Zien (eds.), Semisupervised Learning. MIT Press: Cambridge, MA. 2006

Spectral Dimensionality Reduction
Y. Bengio, O. Delalleau, N. Le Roux, J.-F. Paiement, P. Vincent and M. Ouimet
In Guyon, I., Gunn, S., Nikravesh, M. and Zadeh, L., editors, Feature Extraction, Foundations and Applications, Springer, 2006.

Geometric Methods for Feature Extraction and Dimensional Reduction
C.J.C. Burges
In Data Mining and Knowledge Discovery Handbook: A Complete Guide for Researchers and Practitioners, Eds. O. Maimon and L. Rokach, Kluwer Academic Publishers, 2005

A duality view of spectral methods for dimensionality reduction
Xiao, Lin; Sun, Jun; Boyd, Stephen
23rd International Conference on Machine Learning, ICML 2006

Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering
Yoshua Bengio, Jean-Francois Paiement, Pascal Vincent
NIPS 2004

Learning Eigenfunctions Links Spectral Embedding and Kernel PCA
Y. Bengio, O. Delalleau, N. Le Roux, J.-F. Paiement, P. Vincent and M. Ouimet
Neural Computation, 16(10):2197-2219, 2004.

Isomap

A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, JB; de Silva, V; Langford, JC
Science; 22 Dec. 2000; vol.290, no.5500, p.2319-23

Global Versus Local Methods in Nonlinear Dimensionality Reduction
Vin de Silva, Joshua Tenenbaum
NIPS 2003

Locally linear embedding (LLE)

Nonlinear dimensionality reduction by locally linear embedding
Roweis, ST; Saul, LK
Science; 22 Dec. 2000; vol.290, no.5500, p.2323-6

Think globally, fit locally: Unsupervised learning of low dimensional manifolds
Saul, LK; Roweis, ST
Journal of Machine Learning Research; 15 Feb. 2004; vol.4, no.2, p.119-55

Laplacian eigenmaps

Laplacian eigenmaps for dimensionality reduction and data representation
Belkin, M; Niyogi, P
Neural Computation; June 2003; vol.15, no.6, p.1373-96

Hessian LLE

Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
Donoho, DL; Grimes, C
Proceedings of the National Academy of Sciences of the United States of America; May 13, 2003; v.100, no.10, p.5591-5596

Maximum variance unfolding

Unsupervised learning of image manifolds by semidefinite programming
Weinberger, KQ; Saul, LK
International Journal of Computer Vision; Oct. 2006; vol.70, no.1, p.77-90

Conformal eigenmaps

Analysis and extension of spectral methods for nonlinear dimensionality reduction
Sha, Fei; Saul, Lawrence K.
ICML 2005 - Proceedings of the 22nd International Conference on Machine Learning; 2005; p.785-792

Manifold alignment

Global Coordination of Local Linear Models
S. T. Roweis and L. K. Saul and G. E. Hinton
NIPS 2002

Automatic Alignment of Local Representations
Yee-Whye Teh, Sam Roweis
NIPS 2003

Charting a Manifold
Matthew Brand
NIPS 2003

Non-linear CCA and PCA by Alignment of Local Models
Jakob J. Verbeek, Sam T. Roweis, Nikos Vlassis
NIPS 2004

Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
Zhang, ZY; Zha, HY
SIAM Journal of Scientific Computing; 2005; v.26, no.1, p.313-338

Semisupervised alignment of manifolds
J. H. Ham, D. D. Lee, and L. K. Saul
In Z. Ghahramani and R. Cowell (eds.), Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, pages 120-127. 2005

Spectral graph theory tutorials

Lectures on Spectral Graph Theory (Chapter 1)
F. Chung
BMS Regional Conference Series in Mathematics, No. 92. 1996.

A tutorial on spectral clustering
von Luxburg, U
STATISTICS AND COMPUTING; DEC 2007; v.17, no.4, p.395-416

More papers

Iterative Non-linear Dimensionality Reduction with Manifold Sculpting
Michael Gashler, Dan Ventura, Tony Martinez
NIPS 2008

Random Projections for Manifold Learning
Chinmay Hegde, Michael Wakin, Richard Baraniuk
NIPS 2008

Non-Local Manifold Tangent Learning
Yoshua Bengio, Martin Monperrus
NIPS 2005

Multiple Relational Embedding
Roland Memisevic, Geoffrey Hinton
NIPS 2005

Stochastic Neighbor Embedding
Geoffrey Hinton, Sam Roweis
NIPS 2003

Extreme Components Analysis
Max Welling, Felix Agakov, Christopher K. I. Williams
NIPS 2004

Minimax Embeddings
Matthew Brand
NIPS 2004

Locality Preserving Projections
Xiaofei He, Partha Niyogi
NIPS 2004

Non-Gaussian Component Analysis: a Semi-parametric Framework for Linear Dimension Reduction
Gilles Blanchard, Masashi Sugiyama, Motoaki Kawanabe, Vladimir Spokoiny, Klaus-Robert Muller
NIPS 2006

Learning with Hypergraphs: Clustering, Classification, and Embedding
Dengyong Zhou, Jiayuan Huang, Bernhard Scholkopf
NIPS 2007

Learning to Traverse Image Manifolds
Piotr Dollar, Serge Belongie, Vincent Rabaud
NIPS 2007

Manifold Denoising
Matthias Hein, Markus Maier
NIPS 2007

Optimal Manifold Representation of Data: An Information Theoretic Approach
Denis V. Chigirev, William S. Bialek
NIPS 2004

Linear Dependent Dimensionality Reduction
Nathan Srebro, Tommi Jaakkola
NIPS 2004

Semi-parametric Exponential Family PCA
Sajama, Alon Orlitsky
NIPS 2005

Proximity Graphs for Clustering and Manifold Learning
Miguel A. Carreira-Perpinan, Richard S. Zemel
NIPS 2005

Stratification Learning: Detecting Mixed Density and Dimensionality in High Dimensional Point Clouds
Gloria Haro, Gregory Randall, Guillermo Sapiro
NIPS 2007

Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization
Maxim Raginsky, Svetlana Lazebnik
NIPS 2006