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Summary: RECURSIVE OPTIMIZATION OF AN EXTENDED FISHER
DISCRIMINANT CRITERION
Mayer E. Aladjem
Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev,
P.O.B. 653, 84105 Beer-Sheva, ISRAEL, e-mail: aladjem@bguee.bgu.ac.il
ABSTRACT
A method for recursive optimization of an extended Fisher (ExF) discriminant
criterion is proposed. The method consists of obtaining a discriminant direction which
optimizes the ExF criterion, transforming the data along it into data with greater class
overlap, and iteration to obtain the next discriminant direction. An application to a
medical dataset indicates the potential of the proposed method for finding a sequence
of oblique directions with significant class separation.
1. INTRODUCTION
We discuss discriminant analysis which is carried out by the linear mapping =rTx,
x Rn, R1, n2, with x an arbitrary n-dimensional observation, and r a direction
vector (having unit length rTr=1). The vector r optimizes an extended Fisher (ExF)
discriminant criterion previously proposed by us [1,2]. The optimal vector r is called a
discriminant vector. In this paper our goal is to obtain a sequence of discriminant vectors
by successive optimization of the ExF criterion. In the past, in order to include different
information in the discriminant vectors, an orthogonal constraint on the latter vectors was
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