Research On Multi-view Clustering Algorithm Based On High-order Tensor

Multi-view clustering is an important technique for machine learning,which aims to divide observation data into potential categories by using the data characteristics of multiple views.Since tensor-based clustering analysis can effectively extract high-order correlations across views,the focus of multi-view clustering research has shifted from matrix-based to tensorbased subspace learning.Recently,it has been shown that representing the multi-view data by a tensor and then learning its low-rank or sparse self-expressive tensor is effective.However,there are still some drawbacks to these methods.The algorithms greatly rely on the essential self-expressive tensor learning and ignore the fusion of subspaces.In addition,these algorithms are short of considering the local geometric structure of data,coding the high-order statistics of similarity tensor,and extracting the high-order relation among point pairs when exploring the high-order representation of data.In view of these deficiencies,this thesis engages in academic research on multi-view data fusion learning and effective high-order information extraction.The contributions of this thesis are mainly concentrated in the following aspects:Firstly,this thesis proposes two methods to effectively fuse multi-view information,i.e.,multi-view clustering based on self-expressive tensor learning and manifold learning,and multiview clustering based on self-expressive tensor learning and subspace integration.The former algorithm fuses the common subspace in the Grassmann manifold space,and the latter algorithm fuses the common subspace in the Euclidean space.1)This thesis proposes a multi-view clustering algorithm based on self-expressive tensor learning and manifold learning to overcome the limitations of traditional Euclidean spatial operations.The self-expressive tensor and consensus affinity matrix are modeled by a unified objective function.Thus,the consensus affinity matrix was learned driven by task-oriented design to boost clustering performance.This method not only takes advantage of the complementary information from tensor space but also excavates the superiority of the Grassmann manifold metric on subspace learning;2)this thesis also proposes a self-expressive tensor learning model with a subspace integration strategy to directly learn the consensus subspace across views.The existing clustering algorithms cannot explore the common subspace among all views while learning the self-expressive tensor.In this work,the subspace integration strategy is well added into the optimization model to overcome the defects of subspace representation.Secondly,three multi-view clustering approaches are proposed to boost the performances of clustering through the effective use of high-order information.1)This thesis proposes a novel self-expressive tensor learning model with low-rank constraint and graph constraint to improve the reliability of self-expressive tensor.This method can naturally capture the essential global structure and high-order correlation.Besides,the graph constraint is introduced into the self-expressive tensor learning,which makes the algorithm maintain the local affinity between samples;2)this thesis proposes a multi-view clustering method with a multi-dimensional sparse coding strategy to further extract high-order effective data representation.This algorithm first learns the self-expressive tensor and then uses a multi-dimensional sparse coding model to analyze the high-order statistics in the similarity tensor.Its excellent performance lies in learning novel and essential representation hidden in multi-view data,thus effectively improving the clustering performance;3)this thesis also proposes a multi-view clustering method by extracting two kinds of high-order statistics to fully explore the internal structure of data,i.e.,high-order similarity(samples-to-samples)and high-order correlation(view-to-view).This method effectively combines both within-view and across-view high-order statistics to capture intrinsic structure within the data.Finally,extensive experimental results demonstrate that the proposed methods are effective and practical in multi-view clustering analysis.The methods presented in this thesis well mine the essential structure of multi-view data,significantly improve the performance,and enrich the research contents in machine learning and clustering analysis.