TY - JOUR
T1 - New results on multi-dimensional linear discriminant analysis
AU - Beck, Amir
AU - Sharon, Raz
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Fixed point methods
KW - Generalized eigenvectors
KW - Linear discriminant analysis
KW - Spectral isotonic functions
KW - Superlinear convergence
UR - http://www.scopus.com/inward/record.url?scp=85119479173&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2021.11.003
DO - 10.1016/j.orl.2021.11.003
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AN - SCOPUS:85119479173
SN - 0167-6377
VL - 50
SP - 1
EP - 7
JO - Operations Research Letters
JF - Operations Research Letters
IS - 1
ER -