Disturbance Grassmann Kernels for Subspace-Based Learning
This work addresses robustness issues in subspace-based learning for applications like action recognition, though it is incremental as it builds on existing Grassmann kernels.
The paper tackles the problem of subspace-based learning by addressing the instability of subspaces that can mislead classifiers, proposing Disturbance Grassmann kernels to incorporate potential disturbances for more robust performance. Experiments on action data show these kernels outperform state-of-the-art subspace-based methods, even in adverse conditions.
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.