Research On Rigid Regression And Indicator Matrix Based Subspace Clustering Algorithm

With the advent of the era of big data,the amount of data is also increasing.As an important analysis technology in the direction of data mining and artificial intelligence,cluster analysis technology has been widely developed and applied.The subspace clustering algorithm can effectively process high dimensional data and significantly improve the accuracy of clustering,so it has great research value and broad application prospects.Most existing clustering methods convert raw data into vectors as preprocessing,destroying the spatial information of the data.Discrete indicator matrix in traditional subspace clustering algorithms are directly predicted by continuous clustering indicator matrix resulting in uncertain clustering effects.Therefore,studying how to preserve the spatial information of the data and adopting discrete label matrix clustering can effectively improve the clustering effect.The main works of this paper are as follows:First,in order to solve the two shortcomings in the current mainstream least squares regression subspace clustering algorithms: the vector representation of the original data causes the loss of spatial information in the raw image matrix,and using continuous label clustering to directly predict discrete labels will cause uncertainty in the clustering effect.This paper proposes a subspace clustering algorithm based on image projection rigid regression and indication matrix(SCIPRRIM).This algorithm uses the original matrix of data for clustering,which preserves the spatial information of the data.Image projection ridge regression operation is performed on the original data to find the projection matrix,and the original matrix is reduced in dimension.By alternately optimizing the representation matrix and the projection matrix,the algorithm obtains a representation matrix with the ability to accurately describe the subspace.The adjacency matrix is constructed by the representation matrix,the continuous indicator matrix is replaced by a discrete indicator matrix through a conversion matrix,and the continuous indicator matrix and discrete indicator matrix of the data are alternately optimized to obtain the optimal continuous indicator matrix.The continuous indicator matrix is clustered by K-means to obtain the clustering result.Experimental results show that the clustering effect of the SCIPRRIM algorithm is better than the comparison algorithm,confirming the feasibility of the algorithm.Second,by performing manifold learning to ensure that the representations of sample data on the representation matrix are close to each other,this paper proposes a nonlinear subspace clustering algorithm based on image projection rigid regression and indicator matrix(NSCIPRRIM).The algorithm defines a manifold adjacency matrix to explore the non-linear manifold space of data.By iteratively optimizing the representation matrix,the manifold space learning and the projection matrix learning,a representation matrix capable of accurately characterizing the subspace is obtained.The experimental results show that the clustering effect of NSCIPRRIM algorithm is improved compared with SCIPRRIM algorithm.Third,in order to strengthen the joint learning of discrete labels,subspace representation,and continuous labels,this paper proposes a sparse subspace clustering algorithm based on indicator matrix(SSCIM).The algorithm learns the projection matrix in the row and column directions by constructing the divergence matrix of the image data,and simultaneously projects the row and column directions of the image data to form a new data matrix for clustering,which retains more information of the two-dimensional data.The algorithm solves the shortcoming that the learning of the representation matrix and the learning of the indication matrix are carried out separately.The algorithm alternately optimizes the representation matrix,the continuous indication matrix and the discrete indication matrix,which strengthens the connection between the representation matrix and the discrete indication matrix.Finally,the algorithm constructs the adjacency matrix and introduces the spectral clustering to obtain the final clustering result.Experiments show that the clustering effect of SSCIM algorithm is further improved compared with SCIPRRIM algorithm.