L3/2 Sparsity Constrained Graph Non-negative Matrix Factorization for image representation

For enhancing the cluster accuracy, this paper presents a novel algorithm called L_3/2 Sparsity Constrained Graph Non-negative Matrix Factorization (FGNMF), which based on the convex and smooth L_3/2 norm. When original data is factorized in lower dimensional space using NMF, FGNMF preserves the local structure and intrinsic geometry of data, using the convex and smooth L_3/2 norm as sparse constrains for the low dimensional feature. An efficient multiplicative updating procedure was produced, the relation with gradient descent method showed that the updating rules are special case of its. Compared with NMF and its improved algorithms based on sparse representation, experiment results on USPS handwrite database and COIL20 image database have shown that the proposed method achieves better clustering results.