New results on multi-dimensional linear discriminant analysis

Amir Beck; Raz Sharon

doi:10.1016/j.orl.2021.11.003

New results on multi-dimensional linear discriminant analysis

Amir Beck, Raz Sharon

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Fisher linear discriminant analysis is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. In this paper we concentrate on three different formulations of the multi-dimensional problem. We provide a mathematical explanation why two of the formulations are equivalent and prove that this equivalency can be extended to a broader class of objective functions. The second contribution is a rate of convergence of a fixed point method for solving the third model.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Operations Research Letters
Volume	50
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2021.11.003
State	Published - Jan 2022

Keywords

Fixed point methods
Generalized eigenvectors
Linear discriminant analysis
Spectral isotonic functions
Superlinear convergence

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2021.11.003

Cite this

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abstract = "Fisher linear discriminant analysis is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. In this paper we concentrate on three different formulations of the multi-dimensional problem. We provide a mathematical explanation why two of the formulations are equivalent and prove that this equivalency can be extended to a broader class of objective functions. The second contribution is a rate of convergence of a fixed point method for solving the third model.",

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KW - Fixed point methods

KW - Generalized eigenvectors

KW - Linear discriminant analysis

KW - Spectral isotonic functions

KW - Superlinear convergence

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New results on multi-dimensional linear discriminant analysis

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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