Research On Clustering With Multiple Kernel Concept Factorization

After decades of development,data mining has become an important research area in the field of computer science.Potential knowledge can be exploited from data through data mining.One of the most important methods in data mining is clustering analysis,which is widely used in our daily life.Similarly,clustering analysis has been studied by scholars at home and abroad.The potential structure may be found by clustering,which could be beneficial to many professional fields.By extending matrix factorization into a single non-linear kernel space,Concept Factorization(CF)brings factorization with the help of non-linear functions.It has been widely used for the task of clustering analysis,signal processing and computer vision.However,it is still very difficult to select or design proper kernel function for unknown specific tasks or data sets,because in many cases a single linear or non-linear method can not be embodied the specific characteristics of the task.To alleviate the difficulty of selecting and designing the kernel function in the clustering analysis of concept factorization,we propose two corresponding multiple kernel concept factorization methods,which are as follows:(1)The Global Multiple Kernel Concept Factorization(GMKCF)is proposed.This method integrates multiple candidate kernels linear fusion and concept factorization into a unified learning framework.The benefits are two folds.On the one hand,the result of concept factorization can be improved by using high-quality kernels after integrating.On the other hand,the coefficients of kernels can be better estimated with the guidance of the intrinsic structure detected by concept factorization.This paper designs the corresponding block iteration algorithm and proves its convergence and complexity.Experimental results on the benchmark datasets show the superior of the proposed method.(2)The Discriminative Multiple Kernel Concept Factorization(DMKCF)is proposed.Firstly,we extend the GMKCF to incorporate the important local structure of data.Concretely speaking,we extract the local discriminant structure of data via the local discriminant model with global integration for each base kernel.Moreover,we further linearly combine all these kernel-level local discriminant models to obtain an integrated consensus characterization of the intrinsic structure across base kernels.In this way,it is expected that our method can achieve better results by more compact data reconstruction and more faithful local structure preserving.An iterative algorithm with convergence guarantee is also developed to find the optimal solution.Extensive experiments on benchmark datasets further show that the proposed method outperforms many state-of-the-art algorithms.In summary,this paper focuses on the design of kernel function in concept factorization,and explores new algorithms for generating kernel function in concept factorization.Two multiple kernel clustering algorithms are proposed.Clustering analysis,as the most widely used and common method in pattern recognition,machine learning and data mining,which is also widely used in many professional fields.Therefore,these two multiple kernel clustering methods are of great value both in theory and practice in the field of clustering analysis.