March 2010
Intermediate to advanced
150 pages
7h 13m
English
book
Introduction to Pattern Recognition: A Matlab Approach
by Sergios Theodoridis, Aggelos Pikrakis, Konstantinos Koutroumbas, Dionisis Cavouras
Content preview from Introduction to Pattern Recognition: A Matlab Approach
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6 CHAPTER 1 Classifiers Based on Bayes Decision Theory
1.4 MINIMUM DISTANCE CLASSIFIERS
1.4.1 The Euclidean Distance Classifier
The optimal Bayesian classifier is significant ly simplified under the following assumptions:
• The classes are equiprobable.
• The data in all classes follow Gaussian distributions.
• The covariance matrix is the same for all classes.
• The covariancematrix i s diagonal and all elements across the diagonal are equal.Thatis,S = σ
2
I,
where I is the identity matrix.
Under these assumpt ions, it turns out t hat t he optimal Bayesian classifier is equivalent t o the minimum
Eucl i dean distance classifier. That i s, given an unknown x
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