The aim of the subspace clustering is to segment the high-dimensional data into the corresponding subspace. The structured sparse subspace clustering and the block diagonal representation clustering are quite advanced spectral-type subspace clustering algorithms when handling to the linear subspaces. In this paper, the respective advantages of these two algorithms are fully exploited, and the structured block diagonal representation (SBDR) subspace clustering is proposed. In many classical spectral-type subspace clustering algorithms, the affinity matrix which obeys the block diagonal property can not necessarily bring satisfying clustering results. However, the k-block diagonal regularizer of the SBDR algorithm directly pursues the block diagonal matrix, and this regularizer is obviously more effective. On the other hand, the general procedure of the spectral-type subspace clustering algorithm is to get the affinity matrix firstly and next perform the spectral clustering. The SBDR algorithm considers the intrinsic relationship of the two seemingly separate steps, the subspace structure matrix obtained by the spectral clustering is used iteratively to facilitate a better initialization for the representation matrix. The experimental results on the synthetic dataset and the real dataset have demonstrated the superior performance of the proposed algorithm over other prevalent subspace clustering algorithms.

子空间聚类的目的是将高维数据分割为相应的子空间。当处理线性子空间时，结构化的稀疏子空间聚类和块对角表示聚类是相当先进的频谱类型子空间聚类算法。本文充分利用了这两种算法各自的优点，并提出了结构化块对角表示（SBDR）子空间聚类。在许多经典的光谱类型子空间聚类算法中，服从块对角线属性的亲和矩阵不一定能带来令人满意的聚类结果。但是，kSBDR算法的块对角正则化器直接追求块对角矩阵，并且该正则化器显然更有效。另一方面，频谱类型子空间聚类算法的一般过程是先获取亲和矩阵，然后再进行频谱聚类。SBDR算法考虑了两个看似独立的步骤的内在关系，通过频谱聚类获得的子空间结构矩阵被迭代使用，以促进对表示矩阵的更好初始化。综合数据集和真实数据集上的实验结果证明了该算法优于其他流行子空间聚类算法的性能。