Combining Pattern Classifiers: Methods and Algorithms by Ludmila I. Kuncheva

By Ludmila I. Kuncheva

This identify covers a number of predictive version mixture equipment, for either specific and numeric objective variables (bagging, boosting, etc.). It makes use of particular situations to demonstrate specific issues and makes connection with present literature (many references are from the early 2000s). a few MATLAB resource code is equipped, yet now not on a laptop readable medium.

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The data set is split into training and testing subsets, usually 2/3 for training and 1/3 for testing (the hold-out method). Classifiers A and B are trained on the training set and tested on the testing set. Denote the EXPERIMENTAL COMPARISON OF CLASSIFIERS 19 observed testing accuracies as PA and PB , respectively. This process is repeated K times (typical value of K is 30), and the testing accuracies are tagged with super(1) scripts (i), i ¼ 1, . . , K. Thus a set of K differences is obtained, P(1) ¼ P(1) A À PB (K) (K) to P(K) ¼ PA À PB .

11 (a) Plot of two equivalent sets of discriminant functions: Pðv1 Þpðxjv1 Þ (the thin line), Pðv2 Þpðxjv2 Þ (the dashed line), and Pðv3 Þpðxjv3 Þ (the thick line). (b) Plot of the three posterior probability functions Pðv1 jxÞ (the thin line), Pðv2 jxÞ (the dashed line), and Pðv3 jxÞ (the thick line). In both plots x [ ½0; 10Š. 32 FUNDAMENTALS OF PATTERN RECOGNITION Sometimes more than two discriminant function might tie at the boundaries. Ties are resolved randomly. 5 Bayes Error à Let D be a classifier that always assigns the class label with the largest posterior probability.

4 are 12(N01 þ N10 ). The discrepancy between the expected and the observed counts is measured by the following statistic x2 ¼ ðjN01 À N10 j À 1Þ2 N01 þ N10 (1:11) which is approximately distributed as x2 with 1 degree of freedom. The “21” in the numerator is a continuity correction [14]. ” This error is called Type I error. The alternative error, when we do not reject H0 when it is in fact incorrect, is called Type II error. ” Both errors are needed in order to characterize a statistical test.

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