Graph-Regularized Local Coordinate Concept Factorization for Image Representation

Existing matrix factorization based techniques, such as nonnegative matrix factorization and concept factorization, have been widely applied for data representation. In order to make the obtained concepts to be as close to the original data points as possible, one state-of-the-art method called locality constraint concept factorization is put forward, which represent the data by a linear combination of only a few nearby basis concepts. But its locality constraint does not well reveal the intrinsic data structure since it only requires the concept to be as close to the original data points as possible. To address these problems, by considering the manifold geometrical structure in local concept factorization via graph-based learning, we propose a novel algorithm, called graph-regularized local coordinate concept factorization (GRLCF). By constructing a parameter-free graph using constrained Laplacian rank (CLR) algorithm, we also present an extension of GRLCF algorithm as \(\hbox {GRLCF}_{\mathrm{CLR}}\). Moreover, we develop the iterative updating optimization schemes, and provide the convergence proof of our optimization scheme. Since GRLCF simultaneously considers the geometric structures of the data manifold and the locality conditions as additional constraints, it can obtain more compact and better structured data representation. Experimental results on ORL, Yale and Mnist image datasets demonstrate the effectiveness of our proposed algorithm.