The kernel subspace clustering algorithm aims to tackle the nonlinear subspace model. The block diagonal representation subspace clustering has a more promising capability in pursuing the k-block diagonal matrix. Therefore, the low-rankness and the adaptivity of the kernel subspace clustering can boost the clustering performance, so an adaptive low-rank kernel block diagonal representation (ALKBDR) subspace clustering algorithm is put forward in this work. On the one hand, for the nonlinear nature of the practical visual data, a kernel block diagonal representation (KBDR) subspace clustering algorithm is put forward. The proposed KBDR algorithm first maps the original input space into the kernel Hilbert space which is linearly separable, and next applies the spectral clustering on the feature space. On the other hand, the ALKBDR algorithm uses the adaptive kernel matrix and makes the feature space low-rank to further promote the clustering performance. The experimental results on the Extended Yale B database and the ORL dataset have proved the excellent quality of the proposed KBDR and ALKBDR algorithm in comparison with other advanced subspace clustering algorithms that also are tested in this paper.

核子空间聚类算法旨在解决非线性子空间模型。块对角线表示子空间聚类在追求k-块对角矩阵。因此，核子空间聚类的低秩和自适应性可以提高聚类性能，因此本文提出了一种自适应低秩核块对角线表示（ALKBDR）子空间聚类算法。一方面，针对实际视觉数据的非线性特性，提出了一种核块对角线表示（KBDR）子空间聚类算法。所提出的KBDR算法首先将原始输入空间映射到线性可分的核希尔伯特空间，然后在特征空间上应用谱聚类。另一方面，ALKBDR算法利用自适应核矩阵，使特征空间低秩，进一步提升聚类性能。