Graph-based discriminative concept factorization for data representation

Nonnegative Matrix Factorization (NMF) and Concept Factorization (CF) have been widely used for different purposes such as feature learning, dimensionality reduction and image clustering in data representation. However, CF is a variant of NMF, which is an unsupervised learning method without making use of the available label information to guide the clustering process. In this paper, we put forward a semi-supervised discriminative concept factorization (SDCF) method, which utilizes the limited label information of the data as a discriminative constraint. This constraint forces the representation of data points within the same class should be very close together or aligned on the same axis in the new representation. Furthermore, in order to utilize the local manifold regularization, we propose a novel semi-supervised graph-based discriminative concept factorization (GDCF) method, which incorporates the local manifold regularization and the label information of the data into the CF to improve the performance of CF. GDCF not only encodes the local geometrical structure of the data space by constructing K-nearest graph, but also takes into account the available label information. Thus, the discriminative abilities of data representations are enhanced in the clustering tasks. Experimental results on several databases expose the strength of our proposed SDCF and GDCF methods compared to the state-of-the-art methods.