Research On Subspace Clustering Algorithm With Adaptive Weighted Constraints

In the era of "big data",clustering analysis of high-dimensional image data involves many fields such as computer vision and machine learning.Clustering algorithm based on data self-representation subspace is the key to solve the problem of high-dimensional data clustering,which realizes data mapping from high-dimensional space to low-dimensional subspace and clustering according to linear reconstruction relationship.Among them,the block diagonal structure of coefficient matrix is an important feature to ensure high-precision subspace clustering,but the relatively complex high-dimensional data,the differences of similar data and the similarity of heterogeneous data are more obvious,which will hinder the coefficient matrix from presenting an ideal block diagonal structure.Based on the block diagonal constraint model,this paper proposes an adaptive weighted constraint solution to further improve the block diagonal attribute of the coefficient matrix and improve the clustering effect.The main contributions are as follows:(1)A diagonal representation algorithm of subspace blocks with class weighted constraints is proposed.In order to solve the problem that the existing block diagonal representation model uses K norm to constrain the block diagonal structure of coefficient matrix and ignores the inherent generic information of data,this paper establishes a weighted formula to describe the similarity between classes in data with Euclidean distance between data,and imposes constraints on coefficient matrix.The similarity of similar data is high,and the constraint of class weighting term on corresponding coefficient is relaxed;Heterogeneous data have low similarity and strict constraints on corresponding coefficients.Class weighting constraint uses data generic information to define the weight of coefficient matrix,which improves the description ability of coefficient matrix on intra-class similarity and inter-class difference,and improves the diagonal structure of matrix block to improve clustering ability.(2)A Pearson correlation weighted subspace block diagonal representation algorithm is proposed.In order to solve the problem that the algorithm is sensitive to noise and outliers due to insufficient use of data correlation,this paper constructs the Pearson correlation matrix using the inner product of high-dimensional data vectors to describe the data correlation,and constructs the Pearson penalty matrix through the inverse transformation of the negative exponential function.The penalty matrix is directly weighted coefficient matrix.The higher the data correlation is,the coefficient constraint will be relaxed after the reverse transformation;otherwise,it will be relatively strict.Pearson relation is used in the model to combine the potential correlation of data with the global representation,and the coefficient weighting matrix is constructed according to the paired data correlation to solve the problem that the equal weight coefficient matrix cannot accurately describe the local correlation of data,so as to improve the robustness of the algorithm to the outliers,and then improve the block diagonality of the coefficient matrix and enhance the clustering.(3)Research on application of subspace clustering algorithm.The two seed space algorithms proposed in this paper are combined with spectral clustering to build a clustering model for high dimensional data samples.Through motion segmentation,handwriting recognition,object image and other public data sets,the multi-algorithm comparison experiment was carried out to analyze the clustering performance,time cost,block diagonal and other properties of the model.It was confirmed that after the implementation of weight constraint on the coefficient,especially the introduction of data correlation Pearson weight,the block diagonal structure of the coefficient matrix is more perfect,so as to improve the clustering accuracy.Subsequently,ablation experiments were conducted to analyze the respective contributions of data category information weighting and Pearson relation weighting,which again confirmed the ability of enhancement coefficient matrix to describe data relations and improved clustering.