Constrained concept factorization with graph Laplacian

Abstract

Concept Factorization (CF) is a modified version of Nonnegative Matrix Factorization (NMF) and both of them have been proved to be effective matrix factorization methods for dimensionality reduction and data clustering. However, CF is essentially an unsupervised method which cannot utilize any prior knowledge of data. In this paper, we propose a new semi-supervised concept factorization method, called Constrained Concept Factorization with Graph Laplacian (CCF-GL), which not only incorporates the geometrical information of data, but also utilizes the prior label information to enhance the accuracy of CF. Specifically, we expect that the graph laplacian could preserve the intrinsic manifold structure of original data. Meanwhile, in the low-dimensional space, we hope that data points sharing the same label will have the same coordinate, while the coordinates of data points possessing different labels will be as dissimilar as possible. As a result, the learning quality of this semi-supervised CF method has been significantly enhanced. The experimental results on image clustering show good performance of our algorithm.