Learning Discriminative Stein Kernel for SPD Matrices and Its Applications

TL;DR

This paper introduces a discriminative Stein kernel that optimizes eigenvalues of SPD matrices to improve image classification, outperforming traditional methods by enhancing discrimination and alignment with classification goals.

Contribution

The paper proposes a novel discriminative Stein kernel that adjusts eigenvalues of SPD matrices via learned parameters, improving classification performance.

Findings

Discriminative Stein kernel outperforms original Stein kernel in classification tasks.

Adjusting eigenvalues enhances the discriminative power of SPD matrices.

Experimental results show higher accuracy with the proposed method.

Abstract

Stein kernel has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: i) Eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation; ii) More importantly, eigenvalues only reflect the property of an individual SPD matrix. They are not necessarily optimal for computing Stein kernel when the goal is to discriminate different sets of SPD matrices. To address the two issues in one shot, we propose a discriminative Stein kernel, in which an extra parameter vector is defined to adjust the eigenvalues of the input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three different kernel learning criteria that are commonly used in the literature are employed respectively as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare our proposed discriminative Stein kernel with the original Stein kernel and other commonly used methods for evaluating the similarity between SPD matrices. The experimental results demonstrate that, the discriminative Stein kernel can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original Stein kernel and other commonly used methods.