Research On Multi-View Clustering Methods And Its Applications For Non-linear Data

Multi-view clustering integrates complementary,compatible,complete,and consensus information from multiple views to obtain better clustering results,which has attracted extensive research in the academic community.In multi-view clustering,multi-kernel clustering,as an important branch,is used to mine useful information in nonlinear data.It can implicitly map the original nonlinear data to a high-dimensional Hilbert kernel space through multiple kernel functions to obtain a clear decision boundary,and then use clustering methods to obtain ideal clustering results,providing a guarantee for downstream tasks.Despite the success of such methods in many applications,there are still the following problems:(1)It is difficult to learn a robust and high-quality relationship graph in the kernel space;(2)The learning of the relationship graph and the spectral clustering process are independent of each other,leading to sub-optimal clustering results;(3)Computational and storage costs are high when dealing with high-dimensional nonlinear data.To address these issues,this thesis conducts research on multi-view clustering algorithms for complex and highdimensional nonlinear data to improve clustering performance and apply it to image segmentation.In summary,the main contributions of this thesis are as follows:(1)To address the issue of poor quality of the affinity graph learned in the kernel space,the clustering via multiple kernel k-means coupled graph and enhanced tensor learning(KKG-ETL)is proposed in this thesis.We establish a theoretical connection between spectral clustering and kernel k-means,and innovatively propose the kernelk-means coupling graph learning paradigm to ensure that the affinity graph corresponding to each base kernel has a clear block diagonal structure.Based on this,we introduce tensor learning to explore the similarity between multiple relation graphs and the high-order similarity between views.Finally,we take the forward slice of the tensor as the final relation graph,and input it into the spectral clustering to obtain the final clustering results.(2)To address the problem of sub-optimal clustering results due to the independence of graph learning and clustering processes,we propose a novel multikernel clustering method called one-stage shifted Laplacian refining for multiple kernel clustering(OSLR),which introduces the "one-step framework".Treat each kernel as a graph and then pre-compute its corresponding normalized Laplacian matrix.Considering the energy loss and clustering information retention of the Laplacian reconstruction,an approximate shifted Laplacian(ASL)construction strategy is proposed to transform the traditional Laplacian into ASL,and a set of candidate Laplacians are obtained.Through the above operations,a fine consensus ASL can be learned from these candidate Laplacians.The by-product of Laplacian refinement(clustering indicator)is input into the k-means algorithm to get clustering results.(3)In response to the problem of high storage and computational complexity associated with graph-based learning methods,we propose the cluster center consistency guided sampling learning for multiple kernel clustering(3CSL-MKC).First,a fast singular value decomposition(k-SVD)is employed to obtain the partition matrix for each kernel matrix.Then,based on the principle of cluster center consistency between original points and anchor points,a new dynamic sampling method is proposed to learn optimal anchor points.For each base kernel partition,a low-dimensional representation matrix with consistent clustering information is generated based on dictionary learning with the aid of high-quality anchor points.Finally,by fusing all candidate representation matrices,a consensus representation matrix is obtained and then subjected to the k-means algorithm to obtain the clustering result.The effectiveness and feasibility of the proposed method are further verified through its application in image segmentation.In summary,this thesis presents three systematic clustering methods to address the issues of sub-optimal clustering results and high computational cost in nonlinear data processing.Through comparisons with state-of-the-art methods,the effectiveness and feasibility of the proposed methods have been demonstrated.Therefore,the research results of this thesis have theoretical and practical value for nonlinear data processing.