Local regularization concept factorization and its semi-supervised extension for image representation

Matrix factorization methods have been widely applied for data representation. Traditional concept factorization, however, fails to utilize the discriminative structure information and the geometric structure information that can improve the performance in clustering. In this paper, we propose a novel matrix factorization method, called Local Regularization Concept Factorization (LRCF), for image representation and clustering tasks. In LRCF, according to local learning assumption, the label of each sample can be predicted by the samples in its neighborhoods. The new representation of our proposed LRCF can encode the intrinsic geometric structure and discriminative structure of the high-dimensional data. Furthermore, in order to utilize the label information of labeled data, we propose a semi-supervised version of LRCF, namely Local Regularization Constrained Concept Factorization (LRCCF), which incorporates the label information as additional constraints. Moreover, we develop the corresponding optimization schemes for our proposed methods, and provide the convergence proofs of the optimization schemes. Various experiments on real databases show that our proposed LRCF and LRCCF are able to capture the intrinsic latent structure of data and achieve the state-of-the-art performance.