# Computing the Multivalued Shape of a Pattern Class

## Abstract

The present chapter deals with the problem of determining the pattern class and its multivalued shape/boundary from sampled points (training samples). Once these are computed, some salient features of the class can then be extracted which are useful in making decisions about a course of action (e.g., identification, classification and pattern description) to be taken later. This will also reduce the storage requirement of the complete pattern class.

It may be noted that in most of the real life patter recognition problems, the complete description of a pattern class is not known. Instead, a few sampled points are usually available which are assumed to represent the class. Hence determining the pattern class and its shape from sampled points is an important problem in pattern recognition.

- (i)
As the number of sampled points increases, the extended portions should de- crease.

- (ii)
The extended portions should have less possibility to be in the patter class than the portions explicitly highlighted by the sampled points.

The second property leads to define a multivalued or fuzzy (with continuum grade of belongingness) boundary of a pattern class. The basic concept of one of the existing methods xc1–6 is described below in short for illustration.

## Keywords

Training Sample Sample Group Boundary Variation Coverage Factor Pattern Class## Preview

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