Classification of Multi-dimensional Distributions Using Order Statistics Criteria

Abstract

This paper proposes a novel classification paradigm in which the properties of the Order Statistics (OS) have been used to perform an optimal/near-optimal solution for multi-dimensional problems. In our initial works in [5] and [6], we proposed the foundational theory of CMOS, Classification by the Moments of Order Statistics, for some uni-dimensional symmetric and asymmetric distributions of the exponential family. In this paper, we generalize those results for various multidimensional distributions. The strategy is analogous to a Naïve-Bayes’ approach, although it, really, is of an anti-Naïve-Bayes’ paradigm.We provide here the analytical and experimental results for the two-dimensional Uniform, Doubly-exponential and Gaussian and Rayleigh distributions, and also clearly specify the way by which one should extend the results for higher dimensions.