基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

摘要

针对传统低秩表示聚类方法存在的稀疏性不足及噪声敏感等问题, 提出了一种基于局部图拉普拉斯约束的鲁棒低秩表示聚类模型. 一方面, 通过加入图像数据局部相似性的约束, 在保持表示矩阵分块对角的特性下, 增强了其稀疏性; 另一方面, 从数据相关性的角度分析了低秩表示模型的聚类性质, 通过采用鲁棒低秩表示模型, 不仅降低了噪声的干扰, 而且减弱了表示字典数据之间的线性相关性, 从理论上保证了最终的邻接矩阵具有分块对角的良好聚类性质. 与传统低秩表示方法相比,本文得到的表示矩阵既保证了分块性质,又更加稀疏,仿真实验结果表明聚类效果有明显提升.%Low rank clustering is one of the state-of-art subspace clustering algorithm, but it suffers from dense adjacency map and noise. In this paper, we propose a robust low rank clustering algorithm based on the local graph laplace constraint, which enhances the sparsity of the adjacency matrix while maintain the clustering characteristic; on the other hand, we analyze the mechanics of clustering from the view of incoherence, and argue that the robust model proposed in this paper not only reduce the noise level, but also lower the coherence between data. Finally, experimental results show that our algorithm is more robust and more effective.