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Additional resources for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
T o implement the formal solution requires knowledge of both the a priori probabilities and the conditional densities, and in most pattem recognition problems neither of these is known exactly. Usually, however, sample patterns from each class are available, and the problem is to estimate the discriminant functions from the samples. T h e various procedures available for this task differ in the assumptions they make, and we shall examine a few of the most important procedures. 2. Parametric learning.
However, if used without such assumptions, this measure is far from easy to compute. Many different suggestions have been made for a figure of merit that is both appropriate and at least reasonably easy to compute. These include the ratio of between-class to within-class variance (Miller, 1962), an information or entropy measure (Lewis, 1962; Liu, 1964), divergence (Marill and Green, 1963), mean square error (Tou and Heydorn, 1966), and the Bhattacharyya distance (Kailath, 1967) or Hellinger 24 R.
XN , where xJ = fj noise. Each set of N feature measurements can be represented as an N-dimensional vector x or as a point in the N-dimensional feature space Qx . , m. , m, the function of a statistical classifier is to perform the classification task for minimizing probability of misrecognition. T h e problem of pattern classification can now be formulated as a statistical decision problem (testing of statistical hypotheses) by defining a decision function d(x), + Input Decision Pottern FIGURE I .
Adaptive, Learning and Pattern Recognition Systems: Theory and Applications by Mendel