Theoretical aspects of mapping to multidimensional optimal regions as a multi-classifier

Abstract

Mapping to Multidimensional Optimal Regions (M²OR) is the enhanced version of Mapping to Optimal Regions (MOR) which is a special purposed method for multiclass classification task. Similar to MOR, it reduces computational complexity; however, presents better accuracy. Theoretical and experimental results confirm that by using M²OR, the minimum computational complexity of a multi-classification task is approximately equal to one inner product in feature space. As a multi-classifier, MOR family generalizes the upper bound of Vapnik-Chervonenkis (V.C.) entropy and growth function. Corresponding properties are updated proportionally for real functions. It is shown that V.C. dimension of MOR family is controllable using parameters of the model. With respect to the theorem of Solution Existence, MOR family is able to classify every partitionable feature space.