Classification with the pot-pot plot

TL;DR

This paper introduces a novel supervised classification method using potential functions and a pot-pot plot, demonstrating strong performance and consistency across various benchmark datasets.

Contribution

The paper presents a new classification approach based on potential functions and the pot-pot plot, with extensive analysis of bandwidth selection and comparison to existing methods.

Findings

Method is strongly Bayes-consistent for continuous distributions

Outperforms traditional classifiers like LDA, QDA, and k-NN on benchmark data

Effective across simulated and real datasets

Abstract

We propose a procedure for supervised classification that is based on potential functions. The potential of a class is defined as a kernel density estimate multiplied by the class's prior probability. The method transforms the data to a potential-potential (pot-pot) plot, where each data point is mapped to a vector of potentials. Separation of the classes, as well as classification of new data points, is performed on this plot. For this, either the $\alpha$-procedure ($\alpha$-P) or $k$-nearest neighbors ($k$-NN) are employed. For data that are generated from continuous distributions, these classifiers prove to be strongly Bayes-consistent. The potentials depend on the kernel and its bandwidth used in the density estimate. We investigate several variants of bandwidth selection, including joint and separate pre-scaling and a bandwidth regression approach. The new method is applied to benchmark data from the literature, including simulated data sets as well as 50 sets of real data. It compares favorably to known classification methods such as LDA, QDA, max kernel density estimates, $k$-NN, and $DD$-plot classification using depth functions.