Research For Subspace Clustering Based On Sparse Representation Using Alternating Direction Method

High-dimensional data are prevalent in many areas of machine learning, signal and imageprocessing, computer vision, pattern recognition, etc. However, high-dimensional data are not oftendistributed uniformaly in the ambient space. They lie in or close to low-dimensional structuresinstead. There is a need for data clustering in many applicatons of motion segment and faceclustering. Therefore, the study of high-dimensinal data has a very important sifnificance.Sparse representations of data vectors in the subspaces divide the datas into respectivesubspaces by sparse representation of subspace clustering, which has a good robustness. Firstly,sparse subspace clustering model is analyzed in this paper, and then optimization algorithm of thismodel is focused on the research. Alternating direction method are used to solve sparse subspaceclustering. The experiment on synthetic shows the proposed method have great improvement initeration times and error. The proposed algorithm also can deal with noise.Updating strategy for penalty parameter is propoesed in alternating direction method for sparsesubsapce clustering. Sparse subspace clustering applying to motion segment in a video also isintroduced. The experiments on motion segment show the proposed method have greatimprovement in iteration times and error. The proposed algorithm is also valid for incomplete andnoisy data.Linearized alternating direction with adaptive penalty for sparse subspace clustering is proposed.Sparse subspace clustering is also applied to face clustering. Given face images of multiple subjects,the goal is to find images that belong to the same subject. Face images of multiple subjects lie closeto a linear subspace in this way and face images of the same class belong to the same subspace.Alternating direction method and its improved algorithms are applied to face clustering. Theexperiment on face clustering shows the proposed methods are more effective than other clusreringalgorithm. The proposed optimization algorithm is superior to other algorithms.