Subspace Clustering Modeling And Its Applications

Subspace clustering method reveals the potential subspace structure of high dimensional data by dividing the data into corresponding subspaces.Subspace clustering is widely used in computer vision and machine learning,such as target recognition,motion segmentation,face clustering,image segmentation and so on.In reality,high-dimensional data have such a remarkable feature:high-dimensional data is not without structure,high-dimensional data in essence lies in the union of low-dimensional subspaces.Based on this,subspace clustering methods are based on spectral clustering algorithm,using subspace representation to cluster high dimensional data.Subspace representation model has important influence on clustering performance.This paper focuses on the modeling and solving algorithm of subspace clustering representation model,and explores its application in face clustering,handwritten digits clustering and image segmentation.Image segmentation aims to partition an image into several disjoint regions with each region corresponding to a visual meaningful object.Image segmentation is the image segmentation needs the image features,so the image segmentation problem is transformed into the data clustering problem.So the subspace clustering method provides a good method for image segmentation.The main work of this paper includes:First,a new subspace representation model called Correlation Adaptive Weighted Regression is proposed.We propose an explicit data-correlation-adaptive penalty on the representation coefficients by a combination of correlation weighted l₁-norm andl₂-norm,and formulate the subspace representation as a correlation adaptive weighted regression problem.It can be regarded as a method which interpolates SSC and LSR adaptively depending on the correlation among data samples.The model has the property that the solution is block diagonal and it has grouping effect.These two properties make the model not only have good subspace selection ability,but also can cluster the highly correlated data into a subspace.Second,we use the stability and robustness of nonconvex functions and propose a new subspace representation model by using a nonconvex extension of trace Lasso and a nonconvex approximation of rank function to regularize the subspace representation.The proposed model can adaptively capture the local and the global structure of the subspace representation so that the subspace representation can reveal the real subspace structure of the data and obtain excellent clustering performance.A large number of experiments and objective indicators show that the proposed two models in the face clustering and handwriting digits clustering have achieved satisfactory results.In the image segmentation experiment,the segmentation results accord with human vision,and the objective indexes also show that these two methods are more accurate than other methods.Therefore,the subspace representation models proposed in this paper are a better way to solve the subspace clustering problem.