On Two Simple and Effective Procedures for High Dimensional Classification of General Populations

TL;DR

This paper introduces two simple, effective high-dimensional classification procedures based on determinant and trace criteria, applicable to general populations, with proven asymptotic properties and demonstrated through simulations and real data.

Contribution

The paper extends two classification criteria to general populations, analyzing their asymptotic behavior and demonstrating their effectiveness without requiring variable selection.

Findings

Determinant-based criterion performs well with correlated variables.

Trace-based criterion is effective in small sample, high-dimensional settings.

Both criteria are straightforward to implement and competitive in performance.

Abstract

In this paper, we generalize two criteria, the determinant-based and trace-based criteria proposed by Saranadasa (1993), to general populations for high dimensional classification. These two criteria compare some distances between a new observation and several different known groups. The determinant-based criterion performs well for correlated variables by integrating the covariance structure and is competitive to many other existing rules. The criterion however requires the measurement dimension be smaller than the sample size. The trace-based criterion in contrast, is an independence rule and effective in the "large dimension-small sample size" scenario. An appealing property of these two criteria is that their implementation is straightforward and there is no need for preliminary variable selection or use of turning parameters. Their asymptotic misclassification probabilities are derived using the theory of large dimensional random matrices. Their competitive performances are illustrated by intensive Monte Carlo experiments and a real data analysis.