A General Matrix Function Dimensionality Reduction Framework and Extension for Manifold Learning

Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combinin...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 52; no. 4; pp. 2137 - 2148
Main Authors: Ran, Ruisheng, Feng, Ji, Zhang, Shougui, Fang, Bin
Format: Journal Article
Language:English
Published: United States IEEE 01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Criteria
Cybernetics
Dimensionality reduction
Handwriting
Hyperbolic functions
Laplace equations
Learning systems
Linear functions
Machine learning
manifold learning
Manifolds
Manifolds (mathematics)
Mathematical analysis
matrix function
Pattern classification
Principal component analysis
Reduction
small-sample-size (SSS) problem
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing dimensionality reduction methods and construct a unified criterion function of these methods. Then, combining the unified criterion with the matrix function, we propose a general matrix function dimensionality reduction framework. This framework is configurable, that is, one can select suitable functions to construct such a matrix transformation framework, and then a series of new dimensionality reduction methods can be derived from this framework. In this article, we discuss how to choose suitable functions from two aspects: 1) solving the SSS problem and 2) improving pattern classification ability. As an extension, with the inverse hyperbolic tangent function and linear function, we propose a new matrix function dimensionality reduction framework. Compared with the existing methods to solve the SSS problem, these new methods can obtain better pattern classification ability and have less computational complexity. The experimental results on handwritten digit, letters databases, and two face databases show the superiority of the new methods.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2020.3003620