Disturbance Grassmann Kernels for Subspace-Based Learning

TL;DR

This paper introduces Disturbance Grassmann kernels to improve the robustness of subspace-based classifiers by accounting for potential disturbances in subspace data, leading to better performance in action recognition tasks.

Contribution

It proposes a novel kernel that considers subspace disturbances, extending existing Grassmann kernels, and derives dual optimization for robust subspace classification.

Findings

Proposed kernels outperform state-of-the-art methods.

Robust classifiers handle disturbed subspaces better.

Experiments confirm improved accuracy in action data.

Abstract

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.