By R. Beale
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Additional resources for Neural Computing - An Introduction
Copyright © 1990 IOP Publishing Ltd. STATISTICAL TECHNIQUES 33 Bayesian classification relies on the basic statistical theory of probabilities and conditional probabilities. e. the components of our feature vector) to make an estimate of the likelihood, or probability, of a pattern belonging to a particular class. Let us give some basic definitions; if we let G;, i = 1 , 2 , . . , n be our list of possible groups or classes then we can define the probability of a pattern belonging to a class as P ( G i ) (where 0 5 P(Gj) 5 1).
Using techniques of this kind also has the added advantage of forcing us t o think harder about the statistical nature of the data that we are dealing with in pattern recognition problems. Any method that makes us think long and hard about the nature of the problem with which we are dealing-particularly about the characteristics of the data-cannot be too highly valued. We will make the point early in the book that applying any of the techniques described in this book, with any degree of success, relies heavily on one understanding the nature of the problem in the first place.
30 PATTERN RECOGNITION weight vector. We can see this if we consider the crossover point, or boundary condition, when the output of the classifier is zero. We have: x ~ x w ~ + x ~ x W =~ 0- o Rearranging this gives us: Comparing this to the equation of a straight line (y = mz t c) we can see that the slope of the line is controlled by the ratio of the weight values W1 and W2 and the intercept is controlled by the bias value, 0. Thus far we have proved that if we have the correct value for the weight vector we can indeed perform the discriminating process and set the position of the decision boundary.
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