一种稀疏流形低秩表示的子空间聚类方法

A subspace clustering method based on sparse manifold and lowrank representation

针对基于非负低秩稀疏表示的子空间聚类方法不能准确描述数据集结构的问题,提出了一种稀疏流形低秩表示的子空间聚类方法。该方法使用双曲正切函数代替核范数来估计秩函数,并利用加权稀疏正则项使表示系数矩阵稀疏,同时引入稀疏流形正则项来刻画数据集的内在流形结构信息。首先通过带有自适应惩罚的线性交替方向法求解子空间表示模型。然后利用获得的表示系数矩阵构造相似度矩阵,结合使用谱聚类方法得到数据集的聚类结果,最后采用基于局部和全局一致性的半监督分类方法获得数据集的分类结果。在Extended Yale B数据库、CMU PIE数据库、ORL数据库、COIL 20数据库和MNIST数据库上的实验结果表明,本方法可以提高子空间聚类和半监督学习的准确率。

It is known that the subspace clustering method using the non-negative low rank and sparse representation can not describe the structures of data sets exactly.We propose a new subspace clustering method,based on sparse mani⁃fold and low-rank representation.The method uses the hyperbolic tangent function instead of the nuclear norm to esti⁃mate the rank function,and incorporates a weighted sparse regularizer to approximate the sparse coefficient matrix repre⁃sentation.The sparse manifold regularizer is introduced to describe the inherent manifold structure information of data sets.The subspace representation model is solved by the linearized alternating method with adaptive penalty.We use the obtained representation coefficient matrix to build the affinity matrix,and employ the spectral clustering method to de⁃rive the clustering results of the data sets.Finally,a semi-supervised classification method based on local and global con⁃sistency is used to achieve the classification results of the data sets.Experimental results on the Extended Yale B data⁃base,CMU PIE database,ORL database,COIL 20 database and MNIST database demonstrate that the presented model has potential of improving the accuracy on both the subspace clustering and semi-supervised learning.