Nonnegative local coordinate factorization for image representation.

Recently, nonnegative matrix factorization (NMF) has become increasingly popular for feature extraction in computer vision and pattern recognition. NMF seeks two nonnegative matrices whose product can best approximate the original matrix. The nonnegativity constraints lead to sparse parts-based representations that can be more robust than nonsparse global features. To obtain more accurate control over the sparseness, in this paper, we propose a novel method called nonnegative local coordinate factorization (NLCF) for feature extraction. NLCF adds a local coordinate constraint into the standard NMF objective function. Specifically, we require that the learned basis vectors be as close to the original data points as possible. In this way, each data point can be represented by a linear combination of only a few nearby basis vectors, which naturally leads to sparse representation. Extensive experimental results suggest that the proposed approach provides a better representation and achieves higher accuracy in image clustering.