Research On Kernel Clustering Method Based On Non-negative Subspace Learning

Based on self-expressiveness property,subspace clustering methods have great advantages in processing high-dimensional data and are widely used in computer vision applications.However,most subspace clustering methods are only applicable to linear subspace,and cannot deal with nonlinear data well,while kernel method can make linear inseparable data in the input space become linear separable in the feature space,so the kernel method and subspace learning are combined to apply to clustering tasks.However,current kernel subspace clustering methods generally consist of two steps,firstly,constructing a similarity matrix according to the sample data,and then conducting subsequent clustering tasks.The allocation of cluster members is indirect.To solve this problem,this thesis proposes a non-negative subspace learning method,which changes the membership matrix obtained into a posterior probability of cluster allocation.At convergence,cluster members are directly allocated according to the membership matrix obtained,avoiding the performance instability caused by the post-processing of traditional clustering methods.This method is applied to single-view kernel clustering and multi-view kernel clustering,respectively.The main content and innovative points of the thesis are as follows:(1)Proposed a single-view kernel clustering method based on non-negative subspace learning.For the problem of common subspace clustering models that only consider global structure while neglecting local structure and unstable clustering performance caused by the step-by-step clustering process,this method introduces non-negative Lagrangian relaxation to maintain the non-negativity of the membership matrix and combines the global and local structures of the data samples to learn data similarity and cluster labels in a unified framework.In addition,the model is extended to the kernel space to enhance its ability to handle nonlinear data structures.For optimizing the objective function of this method,a multiplication update rule based on non-negative Lagrangian relaxation is developed,and the convergence is guaranteed in theory.Compared with the traditional spectral clustering subspace methods,the results of this method have shown some improvement on 5 benchmark datasets,which shows the effectiveness of the proposed method.(2)Proposed a multi-view kernel clustering method based on non-negative subspace learning.For the problem of existing multi-view clustering methods neglecting the importance of different views and only clustering through simple view fusion,which affects clustering performance,this thesis extends the single view subspace clustering with non-negative Lagrangian relaxation to multi-view subspace clustering.This method introduces auto weighted multi-view kernel learning,which automatically assigns an optimal weight to the kernel of each view.This method does not force the optimal kernel to be a linear combination of predefined kernels but allows the most suitable kernel to reside in the neighborhood of certain kernels,expanding the search space for the optimal kernel.Experiments have shown that this method can fully mine the complementary information of multi-view and achieve good clustering results.(3)Designed and implemented a non-negative subspace kernel clustering prototype system.This system is completed using the development environment Matlab APP Designer in Matlab.The system is divided into two modules: dataset management and kernel clustering methods,which implement and display the clustering process and results of the two kernel clustering methods.The system can test the effectiveness of the two proposed methods on multiple datasets.