Studies For Several Kinds Of Subspace Clustering Problems Based On Data Reconstruction

The clustering problem,which plays an important role in data processing,is widely used in the computer vision and machine learning communities.The subspace clustering task can be regarded as an extension of the common clustering problem.Based on the property that the observed high dimensional data usually has a low intrinsic dimension,the subspace clus-tering task tries to classify the collected high dimensional data into different low dimensional subspaces.In real word scenario,the collected high dimensional data are usually corrupted by noises,which coves up the real structure of the data.Therefore,the research of the subspace clustering problems is both challenging and an urgent need.In this thesis,we will focus on the subspace clustering problems and provide both algorithm and theoretical analysis of the proposed models.The organization of this thesis is as follows:(1)In Chapter 1,we briefly introduce the research background and significance of subspace clustering,and provide the review for the papers that are close relevant to this thesis.(2)In Chapter 2,a k-support norm regularization based model is proposed,which combines a quadratic data-fidelity and a k-support norm regularization term.The reconstruction error is described by quadratic data-fidelity,and the regularization is used to find the de-sired solution.Under some sound hypotheses,we proved the clustering validity and the statistical recovery guarantee of our model for both clean data and corrupted data.The experiment results show the effectiveness of the new method.(3)Chapter 3 discusses the mixture Gaussian regression with l2 constraint term for subspace clustering.Inspired by the idea that mixture Gaussian distribution can well approach the unknown distribution,we use the mixture Gaussian distribution instead of single peak Gaussian to characterize the noises to suit the complex noise scenario,and employ the l2 norm to trade-off the reconstruction coefficients.Due to the speciality of proposed model,we state that it holds Grouping Effect,and discuss the asymptotic property of the solution.The evaluation result shows that our model achieves the satisfied clustering result on challenging database.(4)For the speciality of multiplicative noise,we design the subspace clustering model under multiplicative noise corruption in Chapter 4.We estimate the clean data and the low rank reconstruction coefficient simultaneously.Then,we use the obtained reconstruction coefficient to perform the subspace clustering.The experiment shows that the proposed model has the satisfied accuracies on the challenging database.(5)In Chapter 5,we make a summarisation of this thesis,and provide the prospects for further work.