On the relationship between the separability measures and the Bayes probability of error
Jovan Dj. Golić · IEEE Transactions on Information Theory · 1987
The information measures, as a special class of efficiency measures of muiticategory information systems, and their relations to the Bayes probability of errorP_{B}have been recently defined and investigated. Another class of efficiency measures called the separability measures is introduced in this paper. The relationship between any separability measure andP_{B}is determined for any2 \leq Q < \infty, whereQdenotes the number of categories in a multicategory information system. As before,\epsilon_{0}and\epsilon_{m}criteria are proposed as the similarity measures between the separability measures andP_{B}. The problems of determination, for any2 \leq Q < \infty, of all the separability measures with minimal\epsilon_{0}and\epsilon_{m}criteria, called\epsilon_{0}-optimal and\epsilon_{m}-Optimal, are defined and completely solved, respectively. The minimal values of\epsilon_{0}and\epsilon_{m}criteria are evaluated as well. It is proved that the information measures are for each3 \leq Q < \inftymore similar toP_{B}than the separability measures with respect to the minimal values of both\epsilon_{0}and\epsilon_{m}criteria. It is pointed out that the average conditional quadratic entropy is not only an information measure but also a separability measure, which is, for each3\leq Q < \infty, \epsilon_{0}-optimal and very close to\epsilon_{m}-optimal separability measures with respect to the\epsilon_{m}criterion.