改进重加权稀疏子空间聚类算法

Evolving reweighted sparse subspace clustering algorithm

稀疏子空间聚类作为先进的子空间聚类算法,不仅能有效地聚类高维数据,而且可以直接对含有噪声、稀疏无关字典等干扰信息的复杂数据进行处理。但是现有的稀疏优化框架都不能很好地满足表示系数矩阵类间稀疏和类内一致的特性。因此,考虑将反正切函数和对数函数的性质同时引入到重加权的l1最小化框架中,使其能够同时满足l0范数在数据较小时斜率趋于无穷、数据较大时斜率趋于零的两个重要特征,从而更好地逼近l0最小化框架,并基于此提出改进的重加权稀疏子空间聚类算法。实验表明相较于其他子空间算法,所提算法有着更好的聚类性能。

As a state-of-the-art subspace clustering algorithm,sparse subspace clustering（SSC）not only can effectively handle high-dimensional data,but also can deal with data nuisances directly,such as noise,sparse outlying entries.However,none of the modified SSC could satisfy the property of sparseness between clusters and consistency within the cluster perfectly.To solve this problem,an evolving iterative weighting（reweighted）l1 minimization framework is proposed,which contains the characteristic of arctan and logarithmic function at the same time.The evolving reweighted l1 minimization framework could simultaneously satisfy the two main features of the l0 minimization framework,which makes a better approximation than the original reweighted l1 minimization.Based on the evolving reweighted l1 minimization framework,a new subspace clustering algorithm is proposed,namely,evolving reweighted SSC.The experiments show that the proposed algorithm could achieve better performance than other subspace clustering algorithms.