Optimized Kernel-based Projection Space of Riemannian Manifolds

TL;DR

This paper introduces an optimized kernel-based projection space for Riemannian manifolds, improving image and video classification by leveraging subspace clustering, dictionary learning, and sparse coding to enhance performance over existing methods.

Contribution

It presents a novel approach to learn an optimized projection space on SPD manifolds using subspace clustering and dictionary learning, outperforming current state-of-the-art techniques.

Findings

Outperforms existing methods on classification tasks.

Demonstrates improved accuracy with the proposed optimized projection.

Validates effectiveness across multiple datasets.

Abstract

It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently, it was shown that embedding such manifolds into a Random Projection Spaces (RPS), rather than RKHS or tangent space, leads to higher classification and clustering performance. However, based on structure and dimensionality of the randomly generated hyperplanes, the classification performance over RPS may vary significantly. In addition, fine-tuning RPS is data expensive (as it requires validation-data), time consuming, and resource demanding. In this paper, we introduce an approach to learn an optimized kernel-based projection (with fixed dimensionality), by employing the concept of subspace clustering. As such, we encode the association of data points to the underlying subspace of each point, to generate meaningful hyperplanes. Further, we adopt the concept of dictionary learning and sparse coding, and discriminative analysis, for the optimized kernel-based projection space (OPS) on SPD manifolds. We validate our algorithm on several classification tasks. The experiment results also demonstrate that the proposed method outperforms state-of-the-art methods on such manifolds.