Least Squares Regression Subspace Clustering For Image Data

In the big data era,it is a common problem for researchers in academia and industrial field that how to process and analysis massive image data with complex characteristics of high dimensionality,redundancy,deficiency,noise,etc.Subspace clustering is an important technique to process and analysis image data,which can find valuable information of image data and have been successfully applied in machine learning,computer vision,etc.Subspace clustering based on least squares regression(LSR)has analytical solution and grouping effect compared to the other subspace clustering methods,such as SSC(Sparse Subspace clustering)and LRR(Low Rank Representation).Therefore,this thesis chooses LSR as a basic clustering model,and then proposes three subspace clustering methods for image data with high dimensionality,redundancy,deficiency,geometric and formal structure.The detail is as follows:1.In the practical applications,image data exists missing values,and missing values completion is the prerequisite of subspace clustering.In general,the missing values are completed before clustering,but this ignores the relationship of completion and clustering.To solve the problem,a joint algorithm of missing value completion and subspace clustering via least squares regression is proposed,which is based on the feedback information of clustering.Experimental results on the motion segmentation data sets with missing values demonstrate that the proposed method can improve clustering accuracy effectively.2.Image data has geometric structure,that is,near neighbor and far neighbor structure.So far,most of existing subspace clustering methods have not used the clustering information of the geometric structure.To solve the problem,with the idea of neighborhood preserving,we propose the least squares regression subspace clustering with geometric structure information(GeoS-LSR),which adds a near neighbor and far neighbor preserving term in the LSR model.And we prove the proposed method can further strengthen grouping effect of LSR theoretically.Experiments on the face image data sets and Hopkins 155 motion segmentation data sets show that GeoS-LSR outperforms existing state-of-the-art clustering methods.3.Image's natural structure is a matrix,but GeoS-LSR and many existing subspace clustering algorithms need to transform the matrix sample into a vector before inputting samples into a clustering model.On the one hand,this transformation will easily lead to"high dimensionality and small size samples" problem,on the other hand,it destroys the natural structure of a sample.To solve the above problem,the weighted-block subspace clustering based on least squares regression(WB-LSR)is proposed,which can preserve samples' original matrix form.Moreover,to avoid the loss of global information while each sample is divided into a lot of local blocks,we propose the transfer subspace clustering via least squares regression(TLSR),which adds a transfer term to WB-LSR.This transfer term can transfer the global information of samples into local blocks.The Research demonstrates that TLSR outperform existing subspace clustering methods and traditional clustering methods.