CLASSIFICATION OF OBJECTS, GIVEN THEIR CLASSIFICATION BY A NUMBER OF CLASSIFIER

Objects may belong to one of s different mutually disjoint classes or categories. The task of assigning an object to one of these classes is called classification in this dissertation. If a number n of classifiers is used then i('th) classifiers will give his decision x(,i) = 0 or 1, or 2 or ... s where x(,i) = 0 means i('th) classifiers failed to give his decision. When all the n classifiers have given their decisions we observe X = (x(,1), ..., x(,n)). The vector X can be mapped into N = (n(,0), n(,1), ..., n(,s)) where n(,i) is the number of x's equal to i . N can be used to take a decision regarding the class x to which the object is to be finally assigned. The n classifiers together with the rule to take decisions constitute a system. Every individual classifiers will have a pattern matrix q('(r)) = (q('(r))(,ij)) where q('(r))(,ij) = P(x(,r) = j (theta) = i). The system will have a pattern matrix Q(n) = (Q(,ij)(n))) where Q(,ij)(n) = P(x = i (theta) = i). Here (theta) is the true class to which this object belongs. The possible rules applied to N discussed in this paper are: (1) the majority rule, (2) the mode rule, (3) sequential rules.;The estimation of Q(n) can be done by using a master set which can be obtained with the help of experts who, we assume, make no mistakes in identifying the objects. Q(n) is good if it has high probabilities of correct classification and low probabilities of misclassification or leaving objects unclassified. How different hypotheses can be tested on Q(n) is discussed in this paper.;The mode rule gives higher values of Q(,ii)(n) compared to the majority rule. Similarly Q(,ij)(n) (i (NOT=) j, j (NOT=) 0) for mode rule is higher than that of majority rule. But Q(,i0)(n) for mode rule is lower than that of the majority rule. Among the 2 sequential rules discussed the first has the same Q(,ij)(n) as the simple majority rule. The second sequential rule discussed takes decisions only for odd values of n, 2 being an exception among even numbers.;In the absence of master set also q('(r)) can be estimated provided there is an expert available whose pattern matrix q is known. The estimators of q('(r)) obtained are asymptotically unbiased. A test on whether q('(r))(,ij) are the same for all r = 1, 2, ..., n is also discussed.