Sparse non-negative matrix factorization with Fractional Norm Constraints

In this paper, we propose a framework for approximate NMF which constrains the L_3/2 norm of the coefficient matrix, called Sparse NMF with Fractional Norm Constraints (NMFFN), which based on the convex and smooth L_3/2 norm. When original data is factorized in lower dimensional space using NMF, NMFFN uses the convex and smooth L_3/2 norm as sparse constrain for the low dimensional feature. An efficient multiplicative updating procedure was produced along with its theoretic justification of the algorithm convergence, the relation with gradient descent method showed that the updating rules are special cases of its. Compared with NMF and its improved algorithms based on sparse representation, experiment results on ORL face database, USPS handwrite database and COIL20 image database have shown that the proposed method achieves better clustering results.