Design of Data-Driven Mathematical Laws for Optimal Statistical Classification Systems

TL;DR

This paper develops data-driven mathematical laws to create optimal statistical classification systems that minimize error rates, using geometric locus methods within a statistical equilibrium framework.

Contribution

It introduces three classes of scalable, data-driven locus equations that generate optimal, statistical classification systems with proven equilibrium properties.

Findings

Three systems of locus equations for optimal classification.

Each class satisfies fundamental statistical laws.

Systems are scalable modules for diverse pattern recognition tasks.

Abstract

This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve minimum error rates for data distributions with unchanging statistics. Thereby, I will design learning machines that minimize the expected risk or probability of misclassification. I will devise a system of fundamental equations of binary classification for a classification system in statistical equilibrium. I will use this system of equations to formulate the problem of learning unknown, linear and quadratic discriminant functions from data as a locus problem, thereby formulating geometric locus methods within a statistical framework. Solving locus problems involves finding equations of curves or surfaces defined by given properties and finding graphs or loci of given equations. I will devise three systems of data-driven, locus equations that generate optimal, statistical classification systems. Each class of learning machines satisfies fundamental statistical laws for a classification system in statistical equilibrium. Thereby, I will formulate three classes of learning machines that are scalable modules for optimal, statistical pattern recognition systems, all of which are capable of performing a wide variety of statistical pattern recognition tasks, where any given M-class statistical pattern recognition system exhibits optimal generalization performance for an M-class feature space.