Research On Adaptive Subspace Clustering Method Based On Least Squares Regression

In the field of data mining,clustering as an important data analysis method attracted widespread attention,but the scale of data continues to expand,the data structure is becoming more and more complex,and the dimensionality is getting higher and higher.It is difficult to use traditional spectral clustering techniques to analysis,subspace clustering is a common method for processing information in a high-dimensional environment,in which the low-dimensional subspace corresponding to the data subset can be accurately found,and the interference of irrelevant information on the clustering result can be removed.Although the existing low-rank representation with adaptive graph regularization method can adaptively learn the data,while retains the global and local information of the data,and obtains a coefficient matrix with a clear cluster structure,but it uses low-rank representation to mine data information,cannot guarantee that the obtained coefficient matrix meets the clustering effect,that is,it has a block diagonal structure.In order to better ensure the block diagonality of the coefficient matrix and improve the robustness of the algorithm to noise,this dissertation conducts in-depth research on the single-view low-rank representation with adaptive graph regularization method based on the least square regression subspace clustering technology.Using the Frobenius norm instead of the kernel norm to approximate the rank function,enhance the clustering effect of the coefficient matrix,make the coefficient matrix reach the block diagonal structure and reduce the computational complexity as much as possible,and then expand it to multi-view scenes.The main research contents include:(1)Introduced subspace clustering algorithm.First,the importance of subspace clustering was explained,and then some common subspace clustering algorithms were discussed,the advantages and disadvantages of several algorithms and their relations were analyzed,and the relevant knowledge of the graph Laplacian matrix was summarized to lead to the Laplacian rank constraint method,which can obtain a coefficient matrix with a clear clustering structure and improve the performance of traditional subspace clustering methods.Finally,the related optimization algorithm of subspace clustering was introduced.(2)A single-view subspace clustering method based on least square regression was proposed.Although the existing low-rank representation with adaptive graph regularization method can better solve the problems of local information missing and unclear graph structure,but it used low-rank representation to mine data information,which makes the obtained coefficient matrix too dense,not conducive to the classification of clusters,and used the kernel norm to constrain the coefficient matrix,which needs to be solved by singular value decomposition,the computational complexity is high,making it difficult to use in practical applications.This dissertation proposes a single-view subspace clustering method based on least squares regression,using the Frobenius norm instead of the kernel norm to approximate the rank function,so that the coefficient matrix have a clustering effect,that is,the coefficients of the cluster-related data are approximately equal,better reveal the true subspace membership,improve clustering performance,and reduce computational complexity.Several real data sets are used to conduct a large number of experiments,and compared with related mainstream methods,the feasibility of the algorithm in this dissertation is verified.(3)The multi-view subspace clustering algorithm based on least square regression was studied.The multi-view subspace clustering algorithm integrates information from multiple views and considers the diversity of different views.In this dissertation,the proposed single-view subspace clustering algorithm based on least squares regression was extended to multi-view data scenarios.By combined least squares subspace clustering and adaptive graph regularization technology,let the learning subspace of different perspectives tends to the common subspace,and finally the rank constraint was imposed on the common subspace,so that it can obtain a good clustering structure while preserving the local structure of each view.And through experiments to verify the clustering effect of the algorithm.