基于亲和矩阵块对角性的子空间聚类

Subspace clustering by block diagonal affinity matrix

近年来,基于谱聚类的子空间聚类方法成为研究热点.由于表示系数矩阵的块对角性能带来亲和矩阵的块对角性,它对于许多基于谱聚类的方法如低秩表示等起着核心作用.因此,基于块对角划分的子空间聚类被提出,但是块对角正则项的运用使得该方法需要添加非负与对称的限制条件,这样会限制表示系数矩阵挖掘数据之间关系的能力.为了解决这个问题,对亲和矩阵使用块对角正则项,提出基于亲和矩阵块对角性的子空间聚类方法.该方法在不限制表示系数矩阵表示能力的同时还保证了亲和矩阵的块对角性.但是对亲和矩阵进行惩罚会使得模型不易求解,幸运的是顺利地求解了模型,并在多个数据集上进行实验,验证了所提出方法的有效性.

In recent years,subspace clustering methods based on spectral clustering have become a research hotspot.Because the block diagonal representation matrix can result in the block diagonal affinity matrix,this block diagonal property plays a key role in many spectral clustering-based methods such as low-rank representation.Therefore,block diagonal representation is proposed.However,the block diagonal regularizer in this method requires the non-negative and symmetric constraint,which will limit the ability of the representation matrix to mine the relationship between data points.To overcome this limitation,we propose a subspace clustering method based on block diagonal affinity matrix by considering block diagonal regularizer for affinity matrix.Our method does not limit the representation ability of the representation matrix,and ensures the block diagonal property of the affinity matrix.However,penalizing the affinity matrix will make the model difficult to solve.Fortunately,we successfully design the numerical algorithm,and conduct experiments on multiple datasets to verify the effectiveness of our proposed method.