Standardizing the comparison of partitions (Q1424639)

A class of \(\arg\max\) classification rules is considered in which a membership function \(m(x,c)\) is attached to each class \(c=1,\dots,G\). An object with predictor value \(x\) is classified to the class \(\hbox{cl}(x)=\arg\max_{c=1,\dots,G} m(x,c)\). (In Bayes classification \(m(x,c)\) are the posterior probabilities to belong to the class \(c\)). The authors propose a standardizing technique for \(m(x,c)\) which allows to compare different \(\arg\max\) classifiers. This technique captures such features of the classifier as non-resemblance (the quality of membership values separation in different classes). Vizualization of the obtained partitions for three (or four) classes is discussed. Results are presented for classification of simulated chi-square distributed r.v.s and for Fisher's Iris data.