Research On Robust Subspace Clustering Algorithm

How to effectively cluster high-dimensional data is a common challenge in modern data analysis.Accurately clustering high-dimensional data sets can be challenging due to the curse of dimensionality,which is a common issue faced by traditional clustering methods.Researchers have developed Subspace Clustering(SC)methods to surmount this problem,which can decompose high-dimensional data sets into multiple low-dimensional subspaces for clustering.thereby effectively reducing the dimensionality of the data and thus improving the accuracy of the clustering.Despite the effectiveness of traditional subspace clustering methods in reducing the dimensionality of high-dimensional data sets,their clustering performance may still be unsatisfactory in the face of data noise,uncertainty,and outliers.Therefore,there is still a need to improve the clustering accuracy of these methods.Therefore,designing robust subspace clustering in the presence of noise,outliers,and uncertainty has become a research hotspot.This thesis mainly focuses on robust subspace clustering methods and designs three robust subspace clustering algorithms,the details of which can be summarized as follows:(1)A Low Rank Representation Algorithm with Robust Affinity MatrixWhen facing noise or outliers in data,the block-diagonal structure of the affinity matrix generated by the Low Rank Representation(LRR)algorithm may not be robust enough to achieve the best clustering performance.To tackle this problem,this thesis proposes a Low Rank Representation Algorithm with Robust Affinity Matrix(LRRRAM)algorithm.Specifically,LRRRAM first applies the LRR algorithm to the data.Then,leveraging the algorithmic idea of Robust Principal Component Analysis(RPCA),the affinity matrix is decomposed into two parts: a clean affinity matrix and noise,in order to obtain a more reliable affinity matrix.Finally,these two parts are incorporated into a unified algorithmic framework.Additionally,an Augmented Lagrangian Multiplier(ALM)-the based algorithm is designed to solve the objective function.Experiments conducted on several datasets have demonstrated that the LRRRAM method proposed in this study exhibits superior performance compared to some existing clustering methods.(2)Clean Robust Affinity Matrix Learning Algorithm for Multi-View ClusteringThis thesis proposes a clean robust affinity matrix learning algorithm for multi-view clustering(CRAA)to solve the problem that the affinity matrix constructed by existing multi-view subspace clustering methods directly using multi-view data is not robust enough.Specifically,CRAA first joins the multi-view data into a joint representation to find a common latent representation space of the multi-view data,which describes the data more comprehensively than individual views.Then,to avoid the influence of various types of outliers on clustering,we impose low-rank and robust principal component analysis constraints on the latent representation space and affinity matrix,respectively.Finally,these two parts are incorporated into a unified algorithmic framework.Additionally,we demonstrate experimentally that the proposed CRAA method outperforms several stateof-the-art approaches in terms of clustering accuracy and robustness,and we propose an ALM-based algorithm to efficiently solve the optimization problem associated with CRAA.(3)Robust Multi-View Subspace Clustering Algorithm with Rank Consistency ConstraintsTo overcome the limitations of the multi-view algorithm model in exploring information consistency among views,a robust multi-view subspace clustering algorithm with rank consistency constraints(CAMR)is proposed in this thesis.Specifically,CAMR first constructs the initial affinity matrix of each view individually.Then cleans the affinity matrix of each view separately using RPCA.Secondly,to maintain the coherence of clustering characteristics across different views,a constraint is imposed on the rank of the affinity matrix of each view,but the direct computation of the rank consistency constraint is costly.To circumvent this,a matrix decomposition technique is employed to break down the affinity matrix of each view,thereby reducing the algorithm’s complexity.Finally,these three steps are integrated into a single optimization framework.In addition,we devise an ALM method to solve CAMR and verify that CAMR has better clustering performance than some state-of-the-art methods on four widely used datasets.