Nonparametric linear discriminant analysis by recursive optimization with random initialization

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Abstract

A method for the linear discrimination of two classes has been proposed by us in [3]. It searches for the discriminant direction which maximizes the distance between the projected class-conditional densities. It is a nonparametric method in the sense that the densities are estimated from the data. Since the distance between the projected densities is a highly nonlinear function with respect to the projected direction we maximize the objective function by an iterative optimization algorithm. The solution of this algorithm depends strongly on the starting point of the optimizer and the observed maximum can be merely a local maximum. In [3] we proposed a procedure for recursive optimization which searches for several local maxima of the objective function ensuring that a maximum already found will not be chosen again at a later stage. In this paper we refine this method.We propose a procedure which provides a batch mode optimization instead an interactive optimization employed in [3]. By means of a simulation we compare our procedure and the conventional optimization starting optimizers at random. The results obtained confirm the efficacy of our method.

Original languageEnglish
Title of host publicationAdvances in Intelligent Data Analysis - 3rd International Symposium, IDA 1999, Proceedings
EditorsDavid J. Hand, Joost N. Kok, Michael R. Berthold
PublisherSpringer Verlag
Pages223-234
Number of pages12
ISBN (Print)3540663320, 9783540663324
DOIs
StatePublished - 1 Jan 1999
Event3rd International Symposium on Intelligent Data Analysis, IDA 1999 - Amsterdam, Netherlands
Duration: 9 Aug 199911 Aug 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1642
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Symposium on Intelligent Data Analysis, IDA 1999
Country/TerritoryNetherlands
CityAmsterdam
Period9/08/9911/08/99

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