Comparison of combinatoric and likelihood ratio procedures for classifying samples

Algorithm AS 271: General Optimal Combinatoric Classification

“…Combinatoric classification was introduced in Zeis and Smith (1974) and developed in Dunn andSmith (1980, 1982) with a further application in Dunn (1982). The algorithm on which subroutine MCE is based is described in detail in Dunn and Smith (1980).…”

“…KMAX must be greater than or equal to I and less than or equal to N input: the a priori probability that an element comes from population I: Al must be greater than 0 and less than I input: misclassification probabilities for each marginal classification rule: entries in the first row are probabilities that an element from popu- lation 1 is misclassified (these entries must be in non-decreasing order); entries in the second row are probabilities that an element from population 2 is misclassified; the ith entry of each row must be associated with the same marginal classification rule the total misclassification probability for the optimal joint classification rule, Of,k,A indicates the optimal classification rule Of k A: the k subscripts in A are stored in the first k entries; entries The algorithm will most frequently be applied when the populations are normally distributed with unequal covariance matrices; additional algorithms facilitating this application appear in Dunn (1992). However, the combinatoric classification procedure requires only that the marginal classification rules be independent with known or estimated misclassification probabilities.…”

“…However, the combinatoric classification procedure requires only that the marginal classification rules be independent with known or estimated misclassification probabilities. Hence, the procedure will lend itself to other applications; one such application is given in Dunn (1982).…”