稀疏子空间聚类的惩罚参数自调整交替方向法

Alternating Direction Method of Self-adjusting Penalty Parameters of Sparse Subspace Clustering

稀疏子空间聚类是利用子空间并集中数据向量的稀疏表示,从而将数据划分到各自子空间,该类方法关键是求出最优稀疏解。文中采用交替方向法求稀疏解,交替方向法把复杂问题分解成简单的、有效求解的子问题,达到最优速度。在交替方向法求解过程中,通常惩罚因子是恒定不变的。文中提出一种惩罚因子参数自调整策略,根据每次迭代信息,调整惩罚因子参数。基于运动分割数据和Hopkins数据库实验,结果表明在迭代次数和运算时间上,稀疏子空间聚类的交替方向法及其惩罚参数自调整策略比传统算法有很大提高,而且对噪声数据也非常有效。

Sparse subspace clustering uses the sparse representation of vectors lying on a union of subspace to cluster the data into separate subspaces. The key of this algorithm is to find the optimal sparse solution. Alternating Direction Method （ ADM） is applied to solve sparse problem in this paper. ADM divides the complex problem into simple and effectively solving sub-problem to achieve optimal speed. In the process of the ADM solving,the penalty factor is constant. In this paper,a penalty factor self-adjusting strategy is proposed, according to the each iterative information,adjust the penalty factor parameters. The experiment based on motion division data and Hop-kins database shows that the proposed method has great improvement in iteration times and computing time compared with traditional al-gorithms,is also valid for noisy data.