Component SPD Matrices: A lower-dimensional discriminative data descriptor for image set classification

TL;DR

This paper introduces CSPD, a new lower-dimensional, discriminative data descriptor for image set classification that leverages Riemannian kernels on SPD matrices to improve classification performance.

Contribution

The paper proposes a novel CSPD framework that divides image sets into sub-image sets and constructs a kernel matrix, enhancing discriminative power and reducing dimensionality.

Findings

CSPD outperforms existing methods on benchmark datasets.

CSPD is lower-dimensional and more discriminative.

The Riemannian kernel satisfies Mercer's theorem, ensuring mathematical validity.

Abstract

In the domain of pattern recognition, using the SPD (Symmetric Positive Definite) matrices to represent data and taking the metrics of resulting Riemannian manifold into account have been widely used for the task of image set classification. In this paper, we propose a new data representation framework for image sets named CSPD (Component Symmetric Positive Definite). Firstly, we obtain sub-image sets by dividing the image set into square blocks with the same size, and use traditional SPD model to describe them. Then, we use the results of the Riemannian kernel on SPD matrices as similarities of corresponding sub-image sets. Finally, the CSPD matrix appears in the form of the kernel matrix for all the sub-image sets, and CSPDi,j denotes the similarity between i-th sub-image set and j-th sub-image set. Here, the Riemannian kernel is shown to satisfy the Mercer's theorem, so our proposed CSPD matrix is symmetric and positive definite and also lies on a Riemannian manifold. On three benchmark datasets, experimental results show that CSPD is a lower-dimensional and more discriminative data descriptor for the task of image set classification.