A branch and bound method solving the max–min linear discriminant analysis problem

Amir Beck*, Raz Sharon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1031-1057
Number of pages27
JournalOptimization Methods and Software
Volume38
Issue number5
DOIs
StatePublished - 2023

Funding

FundersFunder number
Israel Science Foundation92621

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