Recognition of Patterns: Using the Frequencies of Occurrence by Peter W. Becker

By Peter W. Becker

This publication is a revised up-to-date version of the second one version which seemed 1974.The paintings defined during this e-book used to be initiated on the basic electrical Company's Electronics Laboratory, Syracuse, N.Y., U.S.A. the writer wish to take this chance to precise his gratitude to the Electronics Laboratory for its aid and encouragement during this paintings. thank you are particularly because of Dr. J.J. Suran for his endured curiosity and aid. it truly is most unlikely to recognize all of the support the au­ thor has got from individuals of the Laboratory employees. even if, the au­ thor is especially indebted to r·lr. T.C. Robbins for coping with the construct­ ing of the observe recognizer (described in part 7.4) and for lots of aid­ ful discussions. The paintings was once later persisted in Denmark, supported via delivers: no. 1382 in 1966 and no. 1511 in 1967, bought from the Danish Govern­ ment Fund for business and medical study. the writer is thankful to stated Fund, and thereby the Danish taxpayers, who gave the writer a chance for uninterrupted paintings with trend recognitions difficulties. In August 1967 the writer joined the employees of the Electronics Labo­ ratory, Technical college of Denmark, the place the next development attractiveness paintings happened; the writer is worked up to recognize his debt to the participants of the workers and to his scholars for plenty of stimulating and useful discussions.

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P. in a sense may be considered as one attribute with a number of discrete values equal to the product: v1 ' v2• .. • if E1 can take the values 2. 3 or 4. 2 The members of Class A and Class B both with unimodal density functions may be separated by use of one threshold, T. o f8 _ _ Class A probability density function ~ 22 values (2,-1), (2,-5), (3,-1), (3,-5), (4,-1), and (4,-5). The following notation will be used frequently in the remaining part of this report. The probability density function for members of Class A is called fA = fA(~l); fA has the mean a and the variance 0A .

N -1' the p attribute =N which had the smallest incremental effectiveness has thus p been eliminated. Next the IP is computed for the (N p-2) subsets obtained by suppressing one of the retained attributes at a time. The attribute with the smallest incremental effectiveness, say =N -1 is eliminated, etc. p The procedure is continued until only p attributes remain; the set of p attributes is then regarded as being if not the optimum at least a near optimum subset of p attributes. A sequential elimination requires fewer computations than an exhaustive search and experimental evidence (Cardillo and Fu 1967, Paragraphs 1 and 2) tends to indicate that approximately the same subset of p attributes will be obtained by either method.

3). The likelihood method and Bayes' procedure become identical in the often encountered case where (i) all NC a priori probabilities are equal, Ppr(j) = l/Nc, (ii) all NC correct classification costs Kii are equal, and (iii) all NC (N C-l)/2 misclassification costs Kij , iij, 39 are equal. I~hen the likelihood method is used the percentage of correctly clas- sified patterns would be a reasonable index of performance. 5 The Neyman-Pearson Method. ~lhen as before the a priori probabili- ties and the classification costs are not known to the designer and furthermore N~, a special procedure becomes possible.

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