Kurtosis-based projection pursuit for matrix-valued data

TL;DR

This paper introduces a novel projection pursuit method tailored for matrix-valued data, utilizing kurtosis-based indices to effectively identify informative projections, with proven consistency and demonstrated through simulations and real data.

Contribution

It extends classical kurtosis-based projection pursuit to matrix data, proposing two indices that recover optimal projections without label information and establishing their strong consistency.

Findings

Successfully recovers optimal projections for Gaussian mixtures

Demonstrates strong consistency of estimators

Effective on real handwritten postal code data

Abstract

We develop projection pursuit for data that admit a natural representation in matrix form. For projection indices, we propose extensions of the classical kurtosis and Mardia's multivariate kurtosis. The first index estimates projections for both sides of the matrices simultaneously, while the second index finds the two projections separately. Both indices are shown to recover the optimally separating projection for two-group Gaussian mixtures in the full absence of any label information. We further establish the strong consistency of the corresponding sample estimators. Simulations and a real data example on hand-written postal code data are used to demonstrate the method.