Semi-supervised Image Clustering Based On Non-negative Matrix Factorization

Image clustering is a process of dividing a group of image data into clusters so that the data within the cluster are similar to each other but the data between the clusters are not similar.Non-negative Matrix Factorization(NMF)is a method to decompose a non-negative data Matrix into the product of two non-negative factor matrices.NMF is widely used in clustering because of its strong interpretability and good clustering effect.However,traditional NMF is an unsupervised clustering method,where no prior information is used in the clustering process.However,in some practical applications,the data may contain some prior information.The method of using this prior information to guide the clustering is called semi-supervised clustering.Compared with unsupervised clustering methods,semi-supervised clustering can generally obtain more effective clustering results than traditional methods due to the prior information.Based on NMF,three semi-supervised image clustering algorithms are proposed in this paper.First,for the case that NMF cannot use prior information,cannot capture the geometric structure of data,and cannot handle the nonlinear distribution of data,a discriminative graph regular non-negative matrix decomposition(KGDNMNF)with kernel method is proposed.This method constructs the label matrix so that the data with the same label are aligned on the same axis,constructs the graph Laplacian matrix to capture the geometric structure of the data,and uses the kernel method to deal with the case of non-linear distribution of data,which effectively improves the clustering effect.Secondly,generally,the Graph Laplace matrix is constructed based on the original data and may be affected by the noise and outliers in the original data set.Therefore,a discriminative non-negative matrix decomposition(AGDNMF)based on adaptive graph regularization is proposed.This method is also a semi-supervised method,in which the label matrix is also used to constrain the data with the same label to align with the same axis,and the adaptive graph regularization is introduced to produce Laplace matrix in the iteration,which can avoid the influence of noise in the original data set on the experimental results.Third,in addition to the commonly used tag information,there are also paired constraint information.Paired constraint information refers to the known relationship between some data pairs,including must-link,that is,the data pair must belong to the same class,and cannot-link,that is,the data pair must belong to different classes.Based on paired constraint information,a semi-supervised non-negative matrix decomposition(SNMFPC)with acceptance constraint information is proposed.In this method,a loss function is constructed,which requires that the new representation after data decomposition still satisfies the paired constraint information,so as to improve the clustering effect.For the above three methods,the iterative updating formula is given by solving the optimization model,and the experiment verifies that these methods are effective and improve the clustering effect.