Research On Subspace Clustering Method Based On Manifold Regularization And Low-Rank Representation

With the rapid development of information technology,the volume of data has grown,the dimensionality of the data has increased,the scale has grown and the structure has become more complex.How to handle multi-source and multidimensional data has also become a major challenge in the field of data mining.Subspace clustering is an effective way to perform cluster analysis on highdimensional data.Its main idea is to map each sample to its corresponding lowdimensional subspace to reduce the influence of redundant information,thus achieving better clustering performance.In recent years,more and more subspace clustering methods have been proposed.How to obtain the local and global information of the samples is the key to subspace clustering,which is still poses a huge challenge.In this thesis,we conduct a study on subspace clustering based on manifold regularization and low-rank representation.Using both manifold regularization and low-rank representation to capture the global and local structure of the samples during subspace learning,based on a least squares regression method that uses Frobenius norm to constrain the subspace to enhance the coefficient matrix cohesion and to cluster highly correlated data together,thus improving the clustering performance.A further extension of the method is applied to multi-view clustering.The specific work of the thesis is as follows:(1)The basic methods of subspace clustering are studied.The significance of subspace clustering algorithm research and some domestic and international related research on single-view and multi-view subspace clustering algorithms are investigated,and several common and classical algorithms for single-view and multiview subspace clustering are investigated.The relevant theoretical knowledge of subspace clustering is studied in detail,including spectral clustering methods and related techniques such as manifold regularization and Laplace rank constraints,along with an analysis of the relevant optimisation algorithms in the thesis.(2)A single-view subspace clustering method based on manifold regularization and low-rank representation is proposed.To addressing the problem of fusing local structure and global information of samples in subspace clustering,this thesis proposes a subspace clustering method based on manifold regularization and low-rank representation.The method using both manifold regularization and low-rank representation to capture the global and local structure of the samples during subspace learning,and also based on a least squares regression method that uses Frobenius norm to constrain the subspace,and finally achieves optimal partitioning of the data by means of the Laplace rank constraint method.Comparative experiments and analyses with some classical methods on a number of publicly available datasets show that the clustering performance of the method is significantly improved over relevant mainstream methods,while also demonstrating excellent performance in outliers handling.(3)A multi-view common subspace integration clustering method based on manifold regularization and low-rank representation is proposed.In practical applications,multi-view data is common.Compared with single-view data,multi-view data can describe objects more fully from different perspectives or features.The thesis further improves and extends the single-view subspace clustering model based on manifold regularization and low-rank representation for the multi-view data by proposing a multi-view common subspace clustering method.The proposed method takes into account the complementarity of each view and considers that the subspaces of different views have a common structure.In the method,a common subspace is learned from the single subspace learned through manifold regularization and lowrank representation,and a Laplace rank constraint is applied to this common subspace in order to preserve both the local and global structure of the samples,achieve optimal partitioning of the data and improve clustering accuracy.Finally the clustering effectiveness of the method is verified by comparison with the classical method.