Nonconvex Low-Rank Kernel Sparse Subspace Learning for Keyframe Extraction and Motion Segmentation

By exploiting the kernel trick, the sparse subspace model is extended to the nonlinear version with one or a combination of predefined kernels, but the high-dimensional space induced by predefined kernels is not guaranteed to be able to capture the features of the nonlinear data in theory. In this article, we propose a nonconvex low-rank learning framework in an unsupervised way to learn a kernel to replace the predefined kernel in the sparse subspace model. The learned kernel by a nonconvex relaxation of rank can better exploiting the low-rank property of nonlinear data to induce a high-dimensional Hilbert space that more closely approaches the true feature space. Furthermore, we give a global closed-form optimal solution of the nonconvex rank minimization and prove it. Considering the low-rank and sparseness characteristics of motion capture data in its feature space, we use them to verify the better representation of nonlinear data with the learned kernel via two tasks: keyframe extraction and motion segmentation. The performances on both tasks demonstrate the advantage of our model over the sparse subspace model with predefined kernels and some other related state-of-art methods.