Multiple Kernel Clustering Algorithm Based On Subspace Graph Learning

Graphic learning has been widely used in many fields since it has the characteristics of capturing the internal relationship of data and maintaining the data structure,which can have stronger expression ability than the original data.Especially in the field of machine learning,subspace-based graph clustering has shown good performance in many tasks.The key step of graph-based clustering is to construct a graph that can reflect the internal relationship between data,so as to exploit the potential cluster structure information in the data.As an important measure to deal with nonlinear data problems,the kernel method can map the original nonlinear data to the high-dimensional kernel space,where the construct of afifnity graph can better explore the hidden structural information in the data to improve the clustering accuracy.However,how to improve the quality of affinity graph by single kernel method is still an open question.Therefore,the exploration and research of subspace-based graph learning and kernel method have important application value.This paper is devoted to the design of effective algorithms to improve the quality of affinity graph,so as to achieve the purpose of improving the clustering performance.Its main contributions include the following three aspects:(1)A novel Joint Low-rank and Sparse Multiple Kernel subspace Clustering algorithm(JLSMKC)is proposed.Firstly,with combination of low-rank and sparse representation for subspace learning,the affinity graph can obtain the attribute of low-rank and sparse structure.Secondly,a robust multiple kernel low-rank and sparsity constraint model is constructed to reduce the influence of noise on the affinity graph and handle the nonlinear structure of data.Finally,the quality of affinity graph is enhanced by making full use of the consensus kernel via multiple kernel method.The experimental results on seven datasets show that JLSMKC is better than five popular multiple kernel clustering methods in ACCuracy(ACC),Normalized Mutual Information(NMI)and Purity.Meanwhile,the clustering time is reduced and the block diagonal quality of affinity graph is improved.JLSMKC has great advantages in clustering performance compared to the competitors.(2)A pure graph-based multi-kernel clustering algorithm(PGMKC)is proposed.PGMKC skips the excessive pursuit of kernel like JLSMKC and completely focuses on graph learning.It mainly consists of two parts,namely candidate kernel graph learning(CKGL)and kernel graph fusion(KGF).CKGL proposed to directly utilize kernel self-representation property to perform candidate kernel graph learning in multiple reproducing Hilbert kernel spaces,mining and maintaining manifolds embedded in kernel spaces,and generating multiple candidate graphs.KGF uses a flexible self-weighted graph fusion strategy and connectivity constraint to directly generate consensus kernel graph.In addition,an efficient optimization algorithm is proposed to solve PGMKC.A large number of experiments show that the performance of PGMKC is better than the existing multiple kernel clustering methods based on the hybrid of kernel and graph learning.(3)A self-weighted multiple kernel tensor clustering algorithm(AMKTC)is proposed.By using the kernelized self-expressiveness subspace learning(SESL)and multiple base kernels,we first learn multiple candidate graphs in the kernel space.Different from JLSMKC and PGMKC that the structure information of the affinity graph is exploited at the matrix level,AMKTC stacks the candidate graphs into a third-order graph tensor to effectively capture the higher-order correlation between the base kernel data.In order to fully explore the higherorder correlation and reduce the computational complexity,we rotate the tensor along the third dimension.Then,the tensor kernel norm(t-TNN)constraint based on the tensor singular value decomposition(t-SVD)is applied to generate the essential tensor in the kernelized tensor space,so as to exploit the consistent and complementary information between the samples and the candidate graphs.Finally,under the constraint of t-TNN,the nearest neighbor graph weighted fusion strategy is used to assign the optimal contribution weights to the candidate graphs,and an optimal consensus kernel graph is generated.We design an elegant solution algorithm to efficiently solve AMKTC.Experimental results on seven benchmark datasets show that the clustering performance of AMKTC is greatly improved compared with the existing state-ofthe-art methods.To sum up,this paper addresses the problem of graph and multiple kernel learning,exploring its generation method and implementing the information mining from the kernel structure,ie,low-order graph structure and higher-order graph structure.As a basic problem of machine learning and data mining,cluster analysis is widely used in many fields,such as unmanned information retrieval,medical image processing,remote sensing satellite image analysis and so on.In conclusion,the three methods proposed in this paper are of great theoretical and practical value to graph learning and kernel methods.