面向矩阵秩函数准确估计的自表示子空间聚类方法

传统子空间聚类方法通常使用矩阵核范数代替矩阵秩函数进行低秩矩阵恢复，然而在目标优化过程中主要关注低秩矩阵大奇异值的影响，容易导致矩阵秩估计不准确的问题。为此，在分析矩阵奇异值长尾分布特点基础上，提出使用基于截断Schatten-p范数的低秩子空间聚类模型。该模型充分考虑小奇异值对低秩矩阵恢复过程的贡献，利用小奇异值信息拟合矩阵奇异值的长尾分布，通过对矩阵秩函数进行准确估计以提升子空间聚类性能。实验结果表明，与现有加权核范数子空间聚类WNNM-LRR和近邻约束子空间聚类BDR算法相比，在Extended Yale B数据集上的聚类准确性分别提升了11%和8%，所提方法能够更好地拟合数据奇异值分布以及生成准确的相似度矩阵。

Low rank subspace clustering algorithm based on accurate estimation for matrix rank function

Traditional subspace clustering methods usually replace the matrix rank function by the matrix kernel norm to recover the original low rank matrices. However, in the process of minimizing the matrix kernel norm, these algorithms pay too much attention to the calculation of the large singular values of the matrix, resulting in inaccurate estimation of the matrix rank. To this end, this paper analyzed the long tail distribution of matrix singular values and proposed a low rank subspace clustering model based on truncated Schatten-p norm. The proposed model fited the long tail distribution of matrix singular va-lues well and toke full account of the contribution of small singular values to the process of low rank matrix recovery. The model could make full use of small singular values to fit the long tail distribution of matrix singular values, ultimately achieved an accurate estimation of matrix rank function and improved the performance of subspace clustering. The experimental results show that, compared with the WNNM-LRR and BDR subspace clustering algorithms, the proposed method improves the clustering accuracy by 11% and 8% on Extended Yale B dataset, respectively. The proposed method can better fit the distribution of data singular values and construct the similarity matrices more accurately.