Testing for Homogeneity with Kernel Fisher Discriminant Analysis

TL;DR

This paper introduces a kernel-based method for testing homogeneity in reproducing kernel Hilbert spaces, deriving asymptotic null distributions and demonstrating effectiveness through experiments on artificial and real speaker verification data.

Contribution

It develops new test statistics for homogeneity in RKHS, with proven asymptotic properties and practical validation on diverse datasets.

Findings

Accurate asymptotic null distributions derived

Consistent detection of fixed and local alternatives

Effective performance demonstrated on artificial and speaker data

Abstract

We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both artificial data and a speaker verification task is provided.