The condensed nearest neighbor rule using the concept of mutual nearest neighborhood (Corresp.)

Consider a set of N objects, consisting of Ni objects originating from population Ai, i = 1,. . . , k, so that N = Zf-, Ni. In order to classify the set of N objects, we measure a variable with pdf A for objects originating from population Ai. Let x1,x2;. .,x, be the measured values of the N objects, which are assumed to be independent. Now consider the N-tuple Gi = (gljt g2j, * * ’ 3 Sp ’ ’ ’ , gNj), indicating that the object with measured value xi originates from population A,, with gU E { 1,2,* * f ,k} for i= 1,2,* * a, N. The number of elements in Gj with value I is equal to N, (I = $2, + . . , k). A possible classification of the set of N objects can be represented by the N-tuple C=(C*,C~;~~ ,ci; . * , cN), where ci E { 1,2,. . . , k}, indicating that the object with measured value xi is allocated to class ci (there is no restriction on the number of elements in C with a specific value). We find for the mean number of misallocations, given the measured values x,, x2,. . . ,x,, according to C