Hyper-graph regularized discriminative concept factorization for data representation

摘要

For the tasks of pattern analysis and recognition, nonnegative matrix factorization and concept factorization (CF) have attracted much attention due to its effective application to find the meaningful low-dimensional representation of data. However, they neglect the geometry information embedded in the local neighborhoods of the data and fail to exploit the prior knowledge. In this paper, a novel semi-supervised learning algorithm named hyper-graph regularized discriminative concept factorization (HDCF) is proposed. For the sake of exploring intrinsic geometrical structure of the data and making use of label information, HDCF incorporates hyper-graph regularizer into CF framework and uses the label information to train a classifier for the classification task. HDCF can learn a new concept factorization with respect to the intrinsic manifold structure of the data and also simultaneously adapted to the classification task and a classifier built on the low-dimensional representations. Moreover, an iterative updating optimization scheme is developed to solve the objective function of the proposed HDCF and the convergence proof of our optimization scheme is also provided. Experimental results on ORL, Yale and USPS image databases demonstrate the effectiveness of our proposed algorithm.