低秩稀疏亲和矩阵子空间聚类

Low-Rank and Sparse Affinity Matrix for Subspace Clustering

摘要: 子空间聚类在近年来受到了大量的关注，其主要是利用谱聚类的思想学习一个表示系数矩阵以构造亲和矩阵，使用亲和矩阵获得聚类结果。众多方法采用对表示系数矩阵加以限制以保证最终得到的亲和矩阵用于聚类后得到良好的聚类效果，但这种做法会降低亲和矩阵的表示能力。本文提出低秩稀疏亲和矩阵子空间聚类算法，直接对亲和矩阵进行约束以提高表示系数矩阵的表示能力。文章给出了算法的优化过程，验证了结果的块对角性质，在不同数据集上的实验证明了方法的有效性。

Abstract: Subspace clustering has received a lot of attention in recent years, which mainly uses the idea of spectral clustering to learn a representation coefficient matrix to construct an affinity matrix, and uses the affinity matrix to obtain clustering results. Many methods use the restriction of the representation coefficient matrix to ensure that the final affinity matrix is used for clustering to obtain good clustering results, but this practice will reduce the representation ability of the affinity matrix. In this paper, a low-rank sparse affinity matrix subspace clustering algorithm is proposed to directly constrain the affinity matrix to improve the representation ability of the representation coefficient matrix. The optimization process of the algorithm is presented, and the block diagonal property of the results is verified. Experiments on different data sets prove the effectiveness of the method.