Subspace Clustering Of Image Data

With the rapid development of technology,images are widely used.Image data can be got from the image acquisition device,image database and Internet,but more and more image information has been far beyond humans' processing capacity.Moreover,the researches about various image processing technologies have been promoted into a high-speed development period.Because there are usually some relations between the data that got from the reality,which are good for data clustering,the research on image clustering has aroused researchers' interests.Traditional clustering methods cannot be used very well on high-dimensional image data,so subspace clustering method,which is able to deal with high-dimensional data clustering better,becomes a hot issue in the recent research.In this paper,we will investigate three subspace clustering problems on image data,including non-linearity,high-dimensional and structure tensor.Our work is as follows:Firstly,existing subspace clustering methods are usually based on a global linear data set,which express each data point as a linear combination of all other data points.Unfortunately,image data is usually a nonlinear high-dimensional data,which makes traditional subspace clustering poor application.Therefore,motivated by manifold learning of local linear,which express each data point as a linear combination of its k nearest neighbors,and combine with sparse subspace clustering and least squares subspace clustering respectively.Local sparse subspace clustering and local least squares regression subspace clustering are put forward in this paper,which are called local subspace clustering collectively.Local sparse subspace clustering can adjust neighbor points automatically.Further,the numerical results show that the method is obviously effective for clustering of image data.Secondly,traditional clustering methods,which can only be applied on data with vectorization,cannot be applied on two-dimensional image data.In fact,it will damage the internal structure of the original data,i.e.structure tensor,which leads to loss of information that affects the performance of clustering.Moreover,keeping tensor form of the image can also avoid the high-dimensional data after vectorization.It's the fact that the least square regression method based subspace clustering cannot be directly applied on two-dimensional image data,we put forward a two-dimensional least square regression method based on subspace clustering.The main idea is that each pixel on two-dimensional image would be represented by the linear combination,which keeps the integrity of the information.The numerical results show that the method can be directly applied on two-dimensional image data,and the method is stable.Thirdly,two-dimensional least square regression method is only applied on the two-dimensional image data,which is not suitable for high-order tensor data.From the data points in the spatial distribution and the perspectives of image structure tensor,this paper proposes a tensor least square regression method based subspace clustering which can keep the original information as far as possible and strengthen the correlations between the data points to provide strong clustering information.The numerical results show that the proposed method can outperform other clustering methods,which illustrates the correlations between the data points that affect the performance of image clustering.