Research On Fuzzy Kernel Clustering Algorithms Based On DC Programming

As the core technology of data mining,clustering analysis has become more and more important in the research and applications.Different clustering algorithms can be used to solve the different problems.The fuzzy kernel clustering can deal with the the linearly inseparable problems and be robust to noises and outliers,but often obtain local optimum caused by the non-convexity of the objective function.Difference of convex functions programming(DCP)is applied to escape the local optimum.The main contributions of this thesis are summerized as follows:(1)Two kinds of the robust fuzzy kernel clustering algorithms based on DCP are presented,DCP kernel-based fuzzy c-means(DCKFCM)and DCP fuzzy Euler clustering(DCFEC).The robust fuzzy kernel clustering algorithms,represented by the radial basis kernel function and Euler kernel function,transform the objective function into the difference of two convex functions to escape the local optimum and improve clustering performance.The DCP objective function is optimized by the difference of convex functions algorithm(DCA).DCA can not only obtain better solutions efficently,but also maintain the robustness of the algorithm.Experiments on several UCI datasets show the superiority of the robust fuzzy kernel clustering algorithms based on DCP,especially on the large scale datasets.(2)An incomplete data imputation clustering algorithm(DCKFCM-OCS)is proposed by applying DCKFCM to incomplete data clustering.Clustering analysis in the practical application often exists missing data.There are two kinds of clustering methods to process incomplete data,the imputation and the non-imputation,while the imputation methods include filter and embedded techniques.The optimal completion strategy based on kernel-based fuzzy c-means(KFCM-OCS)is a representative imputation algorithm.DCP is applied to optimise the KFCM objective function.Alternative optimization process for DCP clustering and missing completion can obtain a better solution.The convergence of the alternating optimization is proved theoretically.Meanwhile,experiments show the superiority of the improved algorithm,both on the missing completion and clustering performance.