Multi-geometric block diagonal representation subspace clustering with low-rank kernel

Abstract

The popular block diagonal representation subspace clustering approach shows high effectiveness in dividing a high-dimensional data space into the corresponding subspaces. However, existing subspace clustering algorithms have some weaknesses in achieving high clustering performance. This paper presents a multi-geometric block diagonal representation subspace clustering with low-rank kernel (MBDR-LRK) method that includes two major improvements. First, as visual data often exists on a Riemannian manifold not captured by Euclidean geometry, we harness the multi-order data complementarity to develop a multi-geometric block diagonal representation (MBDR) subspace clustering. Secondly, the proposed MBDR-LRK approach ensures the low-rankness in the mapped space, by adapting the kernel matrix to a pre-defined one rather than relying on a fixed kernel as in traditional methods. The paper also presents details on the monotonic decrease of the objective function and the boundedness and convergence of the affinity matrix, and the experimental results prove the convergence of the proposed method. Based on the MATLAB development environment, the proposed MBDR-LRK algorithm outperforms other related algorithms and obtained an accuracy of 88.70% on the ORL (40 classes), 89.39% on the Extended Yale B (38 classes), 50.22% on the AR (100 classes) and 75.47% on the COIL (50 classes) datasets.