The goal of statistical methods for dimensionality reduction is to detect and discover low dimensional structures in high dimensional data. Here, we discuss a recently proposed method, known as Maximum Entropy Unfolding (MEU), for learning faithful low dimensional representations of high dimensional data. This method represents a new perspective on spectral dimensionality reduction and, joined with the theory of Gaussian Markov random fields, provides a unifying prob- abilistic approach to spectral dimensionality reduction techniques. Parameter esti- mation as well as approaches to learning the structure of the GMRF are discussed.

Graphical methods for dimensionality reduction on manifolds

FONTANELLA, Lara;
2013-01-01

Abstract

The goal of statistical methods for dimensionality reduction is to detect and discover low dimensional structures in high dimensional data. Here, we discuss a recently proposed method, known as Maximum Entropy Unfolding (MEU), for learning faithful low dimensional representations of high dimensional data. This method represents a new perspective on spectral dimensionality reduction and, joined with the theory of Gaussian Markov random fields, provides a unifying prob- abilistic approach to spectral dimensionality reduction techniques. Parameter esti- mation as well as approaches to learning the structure of the GMRF are discussed.
2013
9788834325568
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/450489
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