Compressive Classification

TL;DR

This paper analyzes the fundamental limits of compressive classification for Gaussian mixture models, focusing on asymptotic misclassification probability behavior and geometric factors influencing performance.

Contribution

It provides an asymptotic characterization of misclassification probability bounds and introduces geometric concepts analogous to diversity and coding gain for classification.

Findings

Diversity determines the decay rate of misclassification probability in low noise.

Measurement gain depends on geometric properties of source and measurement system.

Diversity and measurement gain can guide dictionary learning for improved classification.

Abstract

This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.