Random-projection ensemble classification

TL;DR

This paper proposes a versatile high-dimensional classification method that combines results from applying base classifiers to random projections, with theoretical guarantees and strong empirical performance.

Contribution

It introduces a novel ensemble classifier based on random projections, with theoretical analysis and empirical validation demonstrating its effectiveness.

Findings

The classifier's excess risk can be controlled independently of original data dimension.

Performance improves as the number of projections increases.

Empirical results show superior finite-sample performance compared to other classifiers.

Abstract

We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one special case that we study in detail, the random projections are divided into disjoint groups, and within each group we select the projection yielding the smallest estimate of the test error. Our random projection ensemble classifier then aggregates the results of applying the base classifier on the selected projections, with a data-driven voting threshold to determine the final assignment. Our theoretical results elucidate the effect on performance of increasing the number of projections. Moreover, under a boundary condition implied by the sufficient dimension reduction assumption, we show that the test excess risk of the random projection ensemble classifier can be controlled by terms that do not depend on the original data dimension and a term that becomes negligible as the number of projections increases. The classifier is also compared empirically with several other popular high-dimensional classifiers via an extensive simulation study, which reveals its excellent finite-sample performance.