Statistical Pattern Classification with Binary Variables

Binary random variables are regarded as random vectors in a binary-field (modulo-2) linear vector space. A characteristic function is defined and related results derived using this formulation. Minimax estimation of probability distributions using an entropy criterion is investigated, which leads to an A-distribution and bilinear discriminant functions. Nonparametric classification approaches using Hamming distances and their asymptotic properties are discussed. Experimental results are presented.

[1]  Edward A. Patrick,et al.  Review of Pattern Recognition in Medical Diagnosis and Consulting Relative to a New System Model , 1974, IEEE Trans. Syst. Man Cybern..

[2]  D. Moore.  Evaluation of Five Discrimination Procedures for Binary Variables , 1973 .

[3]  Solomon Kullback,et al.  Approximating discrete probability distributions , 1969, IEEE Trans. Inf. Theory.

[4]  C A Kulikowski,et al.  A comparison of methods for the automated diagnosis of thyroid dysfunction. , 1971, Computers and biomedical research, an international journal.

[5]  C. Chow.  A class of nonlinear recognition procedures , 1966 .

[6]  JAMES C. STOFFEL,et al.  A Classifier Design Technique for Discrete Variable Pattern Recognition Problems , 1974, IEEE Transactions on Computers.

[7]  Laveen N. Kanal,et al.  Patterns in pattern recognition: 1968-1974 , 1974, IEEE Trans. Inf. Theory.

[8]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[9]  J A Rinaldo,et al.  Symptom diagnosis: optimal subsets for upper abdominal pain. , 1967, Computers and biomedical research, an international journal.

[10]  King-Sun Fu,et al.  Selection and Ordering of Feature Observations in a Pattern Recognition System , 1968, Inf. Control..

[11]  Tzay Y. Young,et al.  Overhead Storage Considerations and a Multilinear Method for Data File Compression , 1980, IEEE Transactions on Software Engineering.

[12]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[13]  Keinosuke Fukunaga,et al.  Estimation of Classification Error , 1970, IEEE Transactions on Computers.

[14]  Tzay Y. Young,et al.  Classification, Estimation and Pattern Recognition , 1974 .

[15]  Tzay Y. Young.  The Reliability of Linear Feature Extractors , 1971, IEEE Transactions on Computers.

[16]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[17]  Tzay Y. Young,et al.  Linear transformation of binary random vectors and its application to approximating probability distributions , 1978, IEEE Trans. Inf. Theory.

[18]  Laveen N. Kanal,et al.  Classification of binary random patterns , 1965, IEEE Trans. Inf. Theory.

[19]  Theodosios Pavlidis,et al.  The editing of picture segmentations using local analysis of graphs , 1977, CACM.

[20]  P. Scheinok,et al.  Symptom diagnosis: the use of two different mathematical models. , 1971, International Journal of Bio-Medical Computing.

[21]  Andrew K. C. Wong,et al.  Typicality, Diversity, and Feature Pattern of an Ensemble , 1975, IEEE Transactions on Computers.

[22]  I. Good.  Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables , 1963 .