Abstract: Based on the low rank representation algorithm, this paper proposes a new model. The new model constructs an affinity graph that reveals the intrinsic relation of the data to complete the clustering task. First of all, this algorithm reproduces the data dictionary by using matrix decomposition principle of the original data, this work can filter out part of the noise. Secondly, the algorithm uses the sparsity of data to strengthen local constraints, and construct nonnegative low rank affinity graphs for given data vectors. The weight of the edge in the affinity graph is obtained from the non-negative low rank sparse coefficient matrix, which is constructed by each data sample as a linear combination of other data samples. The affinity graph thus obtained can show the subspace structure of the data, but also the performance of local linear structure. Finally, the results show that compared with the existing subspace algorithm, the clustering effect of the non-negative local constrained low rank subspace algorithm proposed in this paper is improved obviously.

Key words: subspace clustering, low rank, sparseness, affinity matrix

摘要： 在低秩表示算法的基础上，提出了一个新模型。新模型构建了揭示数据内在特征联系的亲和度图以实现聚类任务。首先，根据矩阵分解原理对原始数据重新生成数据字典，在算法初始输入时筛除部分噪声。其次，利用数据间的稀疏性加强局部约束，为给定的数据向量构建非负低秩亲和度图。亲和度图中边的权重由非负低秩稀疏系数矩阵获得，系数矩阵通过每个数据样本作为其他数据样本的线性组合完成构建，如此获得的亲和度图显示了数据的子空间结构，同时表现局部线性结构。与现存的子空间算法相比，非负局部约束低秩子空间算法在聚类效果上有明显的提升。

关键词: 子空间聚类, 低秩性, 稀疏性, 亲和度矩阵