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

Ran, Ruisheng; Feng, Jiali; Fang, Bin

doi:10.1109/tcyb.2020.3003620

Cited by 17 publications

(8 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main concept of the matrix function framework in [21] is to map the matrices gx, so that the criterion Eq. ( 8) becomes:…”

Section: S Have Different Forms For the Different Methods And Umentioning

confidence: 99%

“…In [21], a general matrix function dimensionality reduction framework is proposed for the dimensionality reduction method in manifold learning.…”

Section: Matrix Function Dimensionality Reduction Frameworkmentioning

confidence: 99%

“…In [21], a general framework for dimensionality reduction based on the manifold was proposed. The main idea of the framework is to use two scalar functions to map the scatter matrices into the corresponding matrix functions, and then to make dimensionality reduction and feature extraction.…”

Section: Introductionmentioning

confidence: 99%

“…This paper aims to solve the SSS problem and improve the classification ability of MFA. So, based on the above idea, i.e., combining the polynomial function and the framework in [21], we proposed a new MFA method, named PMFA (polynomial marginal fisher analysis). Specially, we use two appropriate polynomials to map the scattering matrices of MFA to the new space, which can avoid the SSS problem and get better pattern classification performance.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Marginal Fisher Analysis With Polynomial Matrix Function

Ran

Wang

et al. 2022

IEEE Access

Self Cite

View full text Add to dashboard Cite

Marginal fisher analysis (MFA) is a dimensionality reduction method based on a graph embedding framework. In contrast to traditional linear discriminant analysis (LDA), which requires the data to follow a Gaussian distribution, MFA is suitable for non-Gaussian data, and it has better pattern classification ability. However, MFA has the small-sample-size (SSS) problem. This paper aims to solve the small-sample-size problem while increasing the classification performance of MFA. Based on a matrix function dimensionality reduction framework, the criterion of the MFA method is reconstructed by using the polynomials matrix function transformation, and then a new MFA method is proposed, named PMFA (polynomial marginal fisher analysis). The major contributions of the proposed PMFA method are that it solves the small-sample-size problem of MFA, and it can enlarge the distance between marginal sample points of inter-class, so that it can get better pattern classification performance. Experiments on the public face datasets show that PMFA can get a better classification ability than MFA and its improved methods.INDEX TERMS Dimensionality reduction, manifold learning, marginal fisher analysis, matrix function, the small-sample-size (SSS) problem.

show abstract

“…The main concept of the matrix function framework in [21] is to map the matrices gx, so that the criterion Eq. ( 8) becomes:…”

Section: S Have Different Forms For the Different Methods And Umentioning

confidence: 99%

“…In [21], a general matrix function dimensionality reduction framework is proposed for the dimensionality reduction method in manifold learning.…”

Section: Matrix Function Dimensionality Reduction Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Marginal Fisher Analysis With Polynomial Matrix Function

Ran

Wang

et al. 2022

IEEE Access

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, the exponential locality preserving projection (ELPP) method [11] and a general exponential framework for manifold learning [12], which replace the scatter matrices with matrix exponential. Inspired by the idea of matrix exponential, a more general matrix function is used to map the scatter matrices, and then a general matrix function dimensionality reduction framework is proposed in [13], and thus a Function LPP (FLPP) method is presented, which also solves the SSS problem of LPP.…”

Section: Introductionmentioning

confidence: 99%

Locality Preserving Projections with Autoencoder

Ran¹,

Feng²,

Li³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

<p>The proposed LPPAE method in this paper combines the conventional LPP and Autoencoder creatively. The idea of LPPAE can be made as a general framework and then extended to variants of LPP, so a series of new methods of LPP can be derived. And, the idea of LPPAE can also be extended to the other manifold-based dimensionality reduction methods, for example IsoP, NPE, LLTSA, etc., so that these methods will have new versions and achieve better performance. </p>

show abstract

Fused Local Color Pattern (FLCP): A Novel Color Descriptor for Face Recognition

Karanwal¹

2023

Lecture Notes in Networks and Systems

View full text Add to dashboard Cite

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

Cited by 17 publications

References 54 publications

Marginal Fisher Analysis With Polynomial Matrix Function

Marginal Fisher Analysis With Polynomial Matrix Function

Locality Preserving Projections with Autoencoder

Fused Local Color Pattern (FLCP): A Novel Color Descriptor for Face Recognition

Contact Info

Product

Resources

About