Sparse Nonnegative Matrix Factorization Model Based On PALM Algorithm And Its Application In Face Image Clustering

With the rapid development of image information technology and acquisition tools,people are facing the requirements of analyzing or dealing with all kinds of large-scale data,such as image clustering.Moreover,the dimension of those images is often very high,so it is very difficult to deal with these data effectively.In order to deal with these image data more conveniently and effectively,the most commonly used method is to project the high dimensional image matrix into some low dimensional subspace using proper dimensionality reduction techiques,such that the advanced semantic information hidden in the data and the more low rank effective image expression are learned.Comparing with other dimensionality reduction algorithms,Nonnegative Matrix Factorization?NMF?not only reduce the dimension of the matrix but also extract the hidden information from the high dimensional data.Therefore,it has received lots of attention from the researchers in several academic research fields,and then it has been widely used.In this paper,we mainly improve the nonnegative matrix factorization algorithm from two aspects.First,combining the core idea of nonnegative matrix factorization and sparse coding,the SCAD?Smoothly Clipped Absolute Deviation,SCAD?function is employed as a regularization term.In contrast to other sparsity promoted function,such as ₁L norm,SCAD has the advantages of unbiased,continuous and sparsity.The sparse nonnegative matrix decomposition algorithm based on PALM?sparse nonnegative matrix factorization algorithm based on PALM,NMF_SCAD?is proposed;Second,the NMF_SCAD model is a non-convex constrained optimization problem,the traditional multiplicative updates rules can not converge to the stationary point of original problem.We use the PALM algorithm to solve the NMF_SCAD model,and we give a general form of iteration scheme and prove the stability and convergence of the algorithm.The experimental results show that the clustering algorithm proposed in this paper achieves higher clustering accuracy on different face image datasets.