Data-driven Kernel Subspace Clustering with Local Manifold Preservation

Abstract

Kernel-based subspace clustering methods that can reveal the nonlinear structure of data are an emerging research topic. While advances have been made, existing methods suffer from one or both of the following shortcomings: (1) the predefined kernel determines their performance; (2) they may be vulnerable in arbitrary manifold subspace. In this paper, we propose a novel data-driven kernel subspace clustering model with local manifold preservation, named DKLM. Specifically, DKLM provides an explicit data-driven kernel learning strategy for learning kernel directly from the self-representation of data while satisfying the adaptive-weighting. Based on the kernel, DKLM allows preserving the local manifold structure of data through a kernel local manifold term in nonlinear space and encourages acquiring an affinity matrix with the optimal block diagonal. Various experiments on both synthetic data and real-world data demonstrate the effectiveness of our method.