关键词: 子空间结构范数, 低秩表示, 分组效应, 自适应惩罚的线性化交替法

Abstract: A new unified optimization model is proposed to solve the problem that the Structured Sparse Subspace Clustering can not guarantee the connectivity of the affinity matrix. Firstly, the subspace structured norm of the representation matrix is introduced, and a low-rank representation is added to reveal the global structure of high dimensional data. Secondly, in order to make the affinity matrix to be intra-cluster uniform and inter-cluster sparse, a grouping effect is defined to capture the internal geometric structure of the data. A structured graph regularized low-rank subspace clustering model is proposed. Finally, a linearized alternating method with adaptive penalty（LADMAP） is used to find the optimal solution. The experimental results show that the model can not only capture the global structure of the data, but also capture the intrinsic geometry of the data, forcing the related data to be tightly combined and the uncorrelated data to be loosely separated, so that the affinity matrix and the segmentation matrix become more consistent.

Key words: subspace structure norm, low-rank representation, grouping effect, linearized alternating method with adaptive penalty（LADMAP）