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）

摘要： 针对结构稀疏子空间聚类中不能很好地保证相似度矩阵连接性的问题，给出了一个新的统一优化模型。首先，引入了表示系数矩阵的子空间结构范数，增加了低秩表示来揭示高维数据的全局结构。其次，为了使相似度矩阵具有类内统一，类间稀疏的作用，还定义了分组效应来捕获数据的内部几何结构，提出了结构图正则低秩子空间聚类模型。最后使用自适应惩罚的线性化交替法（LADMAP）来得到最优解。实验结果表明，该模型不但可以捕获数据的全局结构，而且还可以捕获数据的内在几何结构，迫使相关数据紧密结合，不相关数据松散分离，从而使得相似度矩阵与分割矩阵变得更加一致。

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