Subspace Segmentation By K-means Clustering On Low Rank Representations

Clustering has been developing for decades.During this period of time,many related algorithms were formed and published.Graph-based clustering methods proposed in recent ten years have shown most excellent performances in motion segmentation,face clustering and so on.This problem has attracted lots of researcher's interest.Graph-based clustering methods firstly construct an affinity graph for a data set,then use a kind of spectral clustering to compute the final segmentation result.LRR(Low-rank representation)is one of the most representative graph-based methods and alone with its variations have achieved great successes in subspace segmentation tasks.In this paper,we proposed a new clustering method based on the combination of K-means and LRR.The main research contents and achievements of this paper are summarized as follow.(1)A new kind of new structured low-rank representation method is proposed,namely KM-LRR.As the low-rank representations are more capable of revealing the intrinsic structure of an original data set,by conducting K-means on the low-rank representations with a mapping from the original space to a latent space,this new clustering method could obtain better subspace segmentation,which was proven in the experiments in this essay.(2)The proposed algorithm actually builds the connections between K-means and LRR-related algorithms.It also presents the reason why structured LRR methods in matrix factorization mannar outperform the classical LRR algorithm.(3)In the existing matrix factorization low-rank representation methods,determining the intrinsic dimension of the two matrix factors is undiscussed.Based on the deduction in this paper,the rank of the two matrix factors shouldequal the number of the subspaces in KM-LRR.(4)Two variations of KM-LRR are developed in this paper and the relationship with some other existing matrix factorization low-rank representation is discussed.The experiments of clustering on several benchmark databases shows that KM-LRR dominates the related methods(K-means,LRR,FRR)in most cases.