Research Of Graph Representation Clustering Based On Sparse Subspace

As an unsupervised large-scale data processing method,clustering analysis has gradually evolved over many years into various types that are based on partition,density,hierarchy,spectral graph theory,etc.Among them,the method based on spectral graph theory is also known as "graph representation clustering," which can be divided into single-view and multi-view clustering methods according to the number of dataset views.Multi-view clustering can be categorized as complete multi-view and incomplete multi-view clustering according to whether any data feature is missing.The purpose of graph representation clustering is to obtain geometric structure from the original dataset and to learn a consistent,low-dimensional robust graph.Despite being widely applied after years of development,there are still problems in the single-view field,such as ineffective capture of data structure and poor robustness of models against noise and outliers.Multi-view field also has the following drawbacks:(1)Existing methods inability to obtain complete high-order information,latent structure,and complementary information across views;(2)The robustness to noise and outliers need to be improved;(3)The simple binary indicator vector filling method is commonly used to fill the missing features of an incomplete multi-view dataset,resulting in the data structure being destroyed.To address the aforementioned issues,this paper focuses on single-view clustering and incomplete multi-view clustering to deeply study the learning of consistent,low-dimensional,robust graphs.Since the existing single-view clustering methods cannot obtain the complete data structure and assign equal weight to noise and outliers,we propose a novel adaptive graph construction and weighted noise low-rank representation method,called ACLWN.ACLWN includes an adaptive representation graph construction model(ARG)for constructing the initial graph and an adaptive weighted sparse representation graph representation model(AWSG)for obtaining the low-dimensional representation graph of dataset.ARG employs manifold learning and sparse representation to obtain the local data structure.To capture the complete data structure,AWSG introduces several constraints,such as non-negative low-rank,sparsity,and distance regularization terms,and proposes an adaptive weighting matrix to enhance the contribution of important features in the low-dimensional representation graph and improve the robustness of noise and outliers,and finally learn a low-dimensional robust representation graph by employing the latent structure.Furthermore,we experiment on face,object,handwritten digit,and other types of datasets to prove that ACLWN significantly improves clustering performance and practicability.Since the problem that incomplete multi-view methods cannot effectively fill in the missing features and cannot completely obtain the high-order information,latent structure and complementary information across views in incomplete multi-view methods,we propose a novel subspace clustering method based on weighted tensor for incomplete multi-view clustering,called IMSCW.IMSCW includes an adaptive incomplete multi-view data missing value filling method(AMF)to construct complete initial graphs and an incomplete multi-view clustering method based on weighted tensor nuclear norm(WTN)to learn a consistent low-dimensional representation graph.AMF constructs multiple incomplete initial graphs by adaptively selecting k-nearest neighbors to represent the current data,and then fills the missing value by the average similarity value with the non-missing values of the other valid views of the position corresponding to the missing features,so as to ensure the multi-view data structure is complete.WTN first constructs a 3-order tensor from complete initial graphs constructed by AMF,then employs weighted tensor minimization technique to obtain high-order information and latent structure between multi-views of dataset,and finally employs different parameters soft threshold function to shrink singular values so that the eigenvector corresponding to the singular values represents the highly discriminatory features of multi-view dataset.Experimental results on face,text,plant,and scene datasets show that IMSCW has excellent performance in incomplete multi-view clustering fields.The consistent low-dimensional representation graph of IMSCW is robust and suitable for graph representation clustering.