Abstract: Sparse subspace clustering is a newly developed clustering framework for high-dimensional data. Since actual data do not completely satisfy the subspace model assumption, a novel sparse subspace clustering with [k] nearest neighbor constraint is proposed. The proposed algorithm combines the subspace structure, [k] nearest neighbor and the distance information and adds [k] nearest neighbor constraint term into the sparse subspace model. The added term corresponds the intuitive knowledge that closer samples have large similarity coefficients and do not change the sparsity of coefficient matrix. The experimental result on face databases Extended YaleB, ORL, AR, object image database COIL and a handwritten digits database USPS shows that the proposed algorithm has competitive performance.

Key words: subspace, clustering, sparse representation, [k] nearest neighbors, face clustering

摘要： 稀疏子空间聚类是近年提出的高维数据聚类框架，针对实际数据并不完全满足线性子空间模型的假设，提出[k]近邻约束的稀疏子空间聚类算法。该算法结合数据的子空间结构，[k]近邻及距离信息，在稀疏子空间模型上，添加[k]近邻约束项。添加的约束项符合距离越小，相似系数越大的直观认识且不改变系数矩阵的稀疏性。在人脸数据集Extended YaleB、ORL、AR，物体图像数据集COIL20及手写数据集USPS上的聚类实验表明提出的算法具有良好的性能。

关键词: 子空间, 聚类, 稀疏表示, [k]近邻, 人脸聚类