Repeated Observations for Classification

TL;DR

This paper investigates nonparametric classification using repeated observations of feature vectors, proposing simple rules with exponential error convergence and analyzing models like robust detection and linear classification.

Contribution

It introduces classification rules tailored for repeated observations, achieving exponential convergence rates and analyzing specific models in this context.

Findings

Conditional error probabilities decay exponentially with increasing repetitions

Simple classification rules are effective for repeated observation data

Analysis covers models like robust detection, prototype, and linear classification

Abstract

We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size $n$ and relatively low dimension $d$, this paper deals with the situation, when instead of observing a single feature vector $\bX$ we are given $t$ repeated feature vectors $\bV_1,\dots ,\bV_t $. Some simple classification rules are presented such that the conditional error probabilities have exponential convergence rate of convergence as $t\to\infty$. In the analysis, we investigate particular models like robust detection by nominal densities, prototype classification, linear transformation, linear classification, scaling.