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Semi-Supervised Learning$
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Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien

Print publication date: 2006

Print ISBN-13: 9780262033589

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262033589.001.0001

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Spectral Methods for Dimensionality Reduction

Spectral Methods for Dimensionality Reduction

(p.292) (p.293) 16 Spectral Methods for Dimensionality Reduction
Semi-Supervised Learning

Saul Lawrence K.

Weinberger Kilian Q.

Sha Fei

Ham Jihun

Lee Daniel D.

The MIT Press

This chapter provides an overview of unsupervised learning algorithms that can be viewed as spectral methods for linear and nonlinear dimensionality reduction. Spectral methods have recently emerged as a powerful tool for nonlinear dimensionality reduction and manifold learning. These methods are able to reveal low-dimensional structure in high-dimensional data from the top or bottom eigenvectors of specially constructed matrices. To analyze data that lie on a low-dimensional submanifold, the matrices are constructed from sparse weighted graphs whose vertices represent input patterns and whose edges indicate neighborhood relations. The main computations for manifold learning are based on tractable, polynomial-time optimizations, such as shortest-path problems, least-squares fits, semi-definite programming, and matrix diagonalization.

Keywords:   unsupervised learning algorithms, spectral methods, dimensionality reduction, manifold learning, low-dimensional structure, high-dimensional data, polynomial-time optimizations

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