AN INTRODUCTION TO THE DESIGN OF PATTERN RECOGNITION DEVICES

Transcription

1 INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES C 0 U R S E SAN D LEe T U RES - No. 83 PETER W. BECKER T E C H ~ t:niversity I C A L OF DENMARK AN INTRODUCTION TO THE DESIGN OF PATTERN RECOGNITION DEVICES COURSE HELD AT THE DEPARTMENT FOR AUTOMATION AND INFORMATION JULY 1971 UDINE 1971 SPRINGER-VERLAG WIEN GMBH

2 This work IS subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data hanks by Springer-Verlag Wien Originally published by Springer-Verlag Wien - New York in 1972 ISBN DOI / ISBN (ebook)

3 PREFACE It ~ s the purpoae of this paper to introduce the reader to the fundamentals of pattern recognition theory. Having read the paper the reader will have gained an understanding of the problems inherent with design of pattern recognition devices sufficient to form an opinion on practical matters and to appreciate the current literature. The presentation of the theory is kept at an undergraduate level; for the sake of illustration two pattern recognition devices are discussed in some detail in Appendices 1 and 3. In the Addendum the answer is presented to the f o l l o w fi u n ~ g ~ damental answer question in statistical pattern recognition: how does one find the multivariate probability densities which have a specified set of marginals? U d i njuly e ~ 1971

4 GLOSSARY OF SYMBOLS A a B B ( ~ ) b c ~ FOBW IP A class of patterns, Section 2. Sample mean frequency for members of class A, Subsection 5.4. A class of patterns, Section 2. The expected cost of classifying a C.. member with the minimaxingprocedure, Subsection 6.3. Sample mean frequency for members of class B, Subsection 5.4. Pattern class n i of the Nt classes. Frequency of Occurrence of Binary Words, Appendix 4. Average information about classmembership given by 8 1 ; Subsection 5.4. Paragraph (4). Index of Performance, Section 6. The symmetric divergence; Subsection 5.4, Paragraph (5). The cost of classifying a member of class no i as being a member of class no j, Subsection 4.1, Paragraph (b). The average cost incurred when all patterns represented by points in W k are classified as C.members, Subsection The likelihood ratio for micro-region W k, Subsection 6.4. The number of Class A members in the design

5 8 Glossary of symbols M 81) M ST The number of Class A members in the test The number of Class B members in the design The number of Class B members in the test M 5 Measure of Separability, Subsection 5.4. Nt N H Number of pattern classes. The largest number of attributes that can be implemented in the hardware (or software) realization of the pattern recognizer. N p The number of attributes from which the set of p attributes is selected, Subsection 5.6. The probability of a point falling in W k, Sub section 6.1. The probability of a point representing a C. 1 member falling in W k' Sub section PRO p q R(j.) 5 The a priori probability of the appearance of a member of pattern class n i, Subsection 4.1, Paragraph (a). Pattern recognition device. The number of attributes which is used, 3",.., =P' pen H' Figure 1. The number of measurements, T 1,,T q, Figure 1. Bayes' risk; Subsection The expected cost of classifying a Ci member with Bayes' procedure, Subsection 6.2. A Measure of separability, Subsection 5.4.

6 Glossary of Symbols 9 S H The number of hyperplanes, Subsection 7.4. T Thresholdsetting, Figures 2 and 3. W k Micro-region n Ok, Subsection 6.1. =: X ~ The vector with the p coordinates (3 i..., S i.', B p), Section 2. s ~ Attribute not, Figure 1.