On Coarse Graining of Information and Its Application to Pattern Recognition

TL;DR

This paper introduces a classification method using finite mixture models derived from maximum entropy principles and Pythagorean means, with applications demonstrated through distribution examples and discussions on parameter estimation.

Contribution

It presents a novel approach combining maximum entropy and Pythagorean means for deriving mixture model components in classification tasks.

Findings

Derived distributions from Pythagorean family

Demonstrated mixture model application in classification

Discussed parameter and category number estimation

Abstract

We propose a method based on finite mixture models for classifying a set of observations into number of different categories. In order to demonstrate the method, we show how the component densities for the mixture model can be derived by using the maximum entropy method in conjunction with conservation of Pythagorean means. Several examples of distributions belonging to the Pythagorean family are derived. A discussion on estimation of model parameters and the number of categories is also given.