TY - JOUR
T1 - A branch and bound method solving the max–min linear discriminant analysis problem
AU - Beck, Amir
AU - Sharon, Raz
N1 - Publisher Copyright:
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - Fisher linear discriminant analysis (FLDA or LDA) is a well-known technique for dimension reduction and classification. The method was first formulated in 1936 by Fisher in the one-dimensional setting. In this paper, we will examine the LDA problem using a different objective function. Instead of maximizing the sum of all distances between all classes, we will define an objective function that will maximize the minimum separation among all distances between all classes. This leads to a difficult nonconvex optimization problem. We present a branch and bound method for the problem in the case where the reduction is to the one-dimensional space.
AB - Fisher linear discriminant analysis (FLDA or LDA) is a well-known technique for dimension reduction and classification. The method was first formulated in 1936 by Fisher in the one-dimensional setting. In this paper, we will examine the LDA problem using a different objective function. Instead of maximizing the sum of all distances between all classes, we will define an objective function that will maximize the minimum separation among all distances between all classes. This leads to a difficult nonconvex optimization problem. We present a branch and bound method for the problem in the case where the reduction is to the one-dimensional space.
UR - http://www.scopus.com/inward/record.url?scp=85159672574&partnerID=8YFLogxK
U2 - 10.1080/10556788.2023.2198769
DO - 10.1080/10556788.2023.2198769
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AN - SCOPUS:85159672574
SN - 1055-6788
VL - 38
SP - 1031
EP - 1057
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 5
ER -