基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

李波; 卢春园; 冷成财; 金连宝

doi:10.16383/j.aas.2015.c150031

基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

doi: 10.16383/j.aas.2015.c150031

1.
南昌航空大学数学与信息科学学院南昌 330063

基金项目:

国家自然科学基金(61262050,61562062,61363048,61363049),江西省自然科学基金(20151BAB211006)资助

详细信息

作者简介:
卢春园南昌航空大学数学与信息科学学院硕士研究生.主要研究方向为图像处理及数据分析.E-mail:lun_chunyuan@sina.com

冷成财南昌航空大学数学与信息科学学院讲师.主要研究方向为医学图像处理.E-mail:70587@nchu.edu.cn

金连宝南昌航空大学数学与信息科学学院硕士研究生.主要研究方向为图像处理及数据分析.E-mail:jin_lianbao@sina.com

通讯作者:
李波南昌航空大学数学与信息科学学院副教授.主要研究方向为计算机图形学及图像处理.本文通信作者.E-mail:libo@nchu.edu.cn

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出版历程
- 收稿日期: 2015-02-04
- 修回日期: 2015-07-16
- 刊出日期: 2015-11-20

Robust Low Rank Subspace Clustering Based on Local Graph Laplace Constraint

1.
School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063

Funds:

Supported by National Natural Science Foundation of China (61262050, 61562062, 61363048, 61363049) and Natural Science Foundation of Jiangxi Province (20151BAB211006)

摘要

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.
- 低秩聚类 /
- 数据聚类 /
- 图拉普拉斯 /
- 鲁棒主成分分析
Abstract: 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.
- Low rank clustering /
- data clustering /
- graph Laplace /
- robust principle component analysis (RPCA)

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