Riemannian kernel based Nystr\"om method for approximate infinite-dimensional covariance descriptors with application to image set classification

TL;DR

This paper introduces a Riemannian kernel-based Nyström method to efficiently approximate infinite-dimensional covariance descriptors, enhancing image set classification performance on benchmark datasets.

Contribution

It extends the Nyström method to Riemannian manifolds of SPD matrices, enabling practical approximation of infinite-dimensional CovDs for improved classification.

Findings

Outperforms original CovDs on benchmark datasets

Efficient approximation of infinite-dimensional CovDs

Enhances discriminative power in image set classification

Abstract

In the domain of pattern recognition, using the CovDs (Covariance Descriptors) to represent data and taking the metrics of the resulting Riemannian manifold into account have been widely adopted for the task of image set classification. Recently, it has been proven that infinite-dimensional CovDs are more discriminative than their low-dimensional counterparts. However, the form of infinite-dimensional CovDs is implicit and the computational load is high. We propose a novel framework for representing image sets by approximating infinite-dimensional CovDs in the paradigm of the Nystr\"om method based on a Riemannian kernel. We start by modeling the images via CovDs, which lie on the Riemannian manifold spanned by SPD (Symmetric Positive Definite) matrices. We then extend the Nystr\"om method to the SPD manifold and obtain the approximations of CovDs in RKHS (Reproducing Kernel Hilbert Space). Finally, we approximate infinite-dimensional CovDs via these approximations. Empirically, we apply our framework to the task of image set classification. The experimental results obtained on three benchmark datasets show that our proposed approximate infinite-dimensional CovDs outperform the original CovDs.