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.

该研究聚焦于子空间学习问题，提出了三种新的核函数：Disturbance Grassmann（DG）核、与子空间矩阵有关的干扰的投影核和基的奇异值干扰的投影核，以应对现有算法中忽视子空间不稳定性的问题，实验表明所提出的核相比现有基于子空间的方法表现更佳。