Abstract:

This paper presents a novel algorithm called L_3/2 regularized graph nonnegative matrix factorization, which was based on the convex and smooth L_3/2 norm. When original data is factorized in lower dimensional space by nonnegative matrix factorization, L_3/2 regularized graph nonnegative matrix factorization preserves the local structure and intrinsic geometry of data, with the aid of  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. Compared with nonnegative matrix factorization and its improved algorithms based on sparse representation, the proposed method achieves better clustering results, which is shown by experiment results on ORL face database, USPS handwrite database, and COIL20 image database.

Key words: image clustering, sparse representation, nonnegative matrix factorization, regularized