Research On Multiple Kernel Clustering Based On Block-diagonal Representation

With the advancement of technology,people have increasingly diverse channels to access information,and the ways information is stored are becoming more varied.As a result,people are faced with increasingly large data scales and increasingly complex data structures.Because of the ability to capture the nonlinear structure of data,multiple kernel clustering methods provide a strong support for processing and analysing complex data and achieve good results.Multiple kernel clustering methods fuse multiple kernel functions(base kernels)to generate an optimal kernel by a kernel weight strategy,and their clustering performance mainly depends on the quality of the optimal kernel.However,most of the existing multiple kernel clustering methods result in the low quality of the optimal kernel due to the kernel weight strategy,which ultimately affects the clustering effect.In addition,there are still some key problems to be solved in the existing multiple kernel clustering research,such as clustering bias caused by multiple-step learning,the influence of complex data structure on the accuracy of clustering results,and the effective clustering of incomplete data.In response to the issues mentioned above,this thesis combines multiple kernel learning,block-diagonal representation,local kernel selection,graph learning and data imputation to conduct in-depth research,and aims to propose multiple kernel clustering methods with better clustering performance.The main work and contributions of this thesis are as follows:(1)A multiple kernel k-means clustering method based on block-diagonal representation is proposed.In view of the low quality of the optimal kernel and clustering bias caused by multiple-step learning strategy,a multiple kernel k-means clustering method based on block-diagonal representation is proposed in this thesis.On one hand,an adaptive kernel weight strategy is introduced based on the relationship between base kernels and the optimal kernel.This strategy dynamically updates the weights of base kernels to generate an optimal kernel.It fully utilizes the role of each base kernel in generating the optimal kernel and balances their contributions,assigning a reasonable weight to each base kernel,thereby promoting the quality of the optimal kernel.On the other hand,using the Laplacian matrix and relevant properties of matrix eigenvalues,a block-diagonal representation of the product of an indicator matrix and its transpose is obtained.This block-diagonal regularization term enhances the product matrix to possess a block-diagonal structure,allowing direct clustering results to be derived from the indicator matrix,achieving one-step clustering.By combining the above two hands,this proposed method can improve the quality of the optimal kernel,thus improve the clustering performance.Moreover,one-step clustering can be realized to ensure the reliability of the final clustering results.In addition,the experimental results indicate that the clustering results of the proposed method are superior to comparison methods.(2)A multiple kernel clustering method with structure-preserving and block diagonal property is proposed.Data in real world often exhibit complex intrinsic structures.However,the previous research work and most existing multiple kernel clustering methods pay little attention to the intrinsic structure of the data,which inevitably affects the accuracy of clustering results.To address this issue,a multiple kernel clustering method with structurepreserving and block-diagonal property is proposed based on graph learning theory in this thesis.On one hand,this method maintains the global structure of the data in the kernel space through the self-expression of the affinity matrix.On the other hand,it preserves the local structure of the data in the kernel space by accurately measuring the similarity between data points in the kernel space.Combining these two hands,the method can keep the real intrinsic structure of data.Additionally,graph theory is utilized to obtain a block-diagonal representation of the affinity matrix,which encourages the affinity matrix has clear clustering results and enables one-step clustering.Furthermore,the kernel weight strategy from the previous research is employed to ensure the quality of the optimal kernel.In summary,this proposed method not only achieves a high-quality optimal kernel,but also obtains a high-quality affinity graph,thereby enhancing clustering performance.The experimental results also demonstrate that the clustering performance of this proposed method is superior to comparison methods.(3)A block-diagonal multiple kernel k-means clustering method that combines local kernels and a neighborhood kernel is proposed.The two aforementioned research works both select all base kernels to generate an optimal kernel,without considering the similarity between base kernels.This may result in the redundancy of base kernels.Although there have been some multiple kernel clustering methods that select local base kernels to generate the optimal kernel,they rarely combine a local kernel method and a neighborhood kernel method to generate the optimal kernel.By not integrating the advantages of the two methods,the quality of the optimal kernels may not be effectively improved.To address this issue,a block-diagonal multiple kernel k-means clustering method is proposed by combining a local kernel method and a neighborhood kernel method in this thesis.This method selects base kernels with low similarity to generate a consensus kernel by using a localized kernel selection strategy,overcoming the redundancy and preserving the diversity of base kernels.And it selects a neighborhood kernel of the consensus kernel as the optimal kernel to expand the search range for the optimal kernel.Additionally,by imposing a block-diagonal constraint on the product of the indicator matrix and its transpose,one-step clustering is achieved.By integrating the local kernel method and the neighborhood kernel method,this proposed method further enhances the quality of the optimal kernel.Moreover,one-step clustering ensures the reliability of the final clustering results.The experimental results demonstrate the effectiveness of this proposed method in achieving good clustering performance.(4)A block-diagonal multiple kernel clustering method for incomplete multi-view data is proposed.Due to various objective reasons,data in practical problems may often be incomplete.The three aforementioned works and most existing multiple kernel clustering methods focuse on clustering with complete data and rarely explore clustering with incomplete data.Even in relevant researches,there are often issues such as low quality of the optimal kernel and clustering bias caused by multiple-step learning.A block-diagonal multiple kernel k-means clustering method is proposed for incomplete multi-view data in this thesis.This method keeps the existing data unchanged while imputing the missing data to obtain base kernels.The optimal kernel is then generated by using the kernel weight strategies based on the base kernels and the consensus base kernels.In addition,a block-diagonal constraint is imposed on the product of the indicator matrix and its transpose to achieve one-step clustering.By integrating data imputation,optimal kernel learning,and indicator matrix learning into a unified model,this proposed method achieves one-step clustering,and achieves effective clustering for incomplete multi-view data.The experimental results indicate that the clustering performance of this proposed method is superior to comparison methods.