Directional consistency and Relational consistency Concept Factorization for Text Clustering

Abstract: This Paper is to extract the underlying concepts which are consistent with the low-dimensional manifold structure with the hope that this will facilitate further processing, such as clustering. Central to our approach is a graph model which captures the local geometry of the text submanifold. Thus, we call it Locally Consistent Concept Factoriaztion.The graph Laplacian, analogous to the Laplace-Beltrami operator on manifolds, can be used to smooth the text-to-concept mapping. Thus, the obtained concepts can well capture the intrinsic geometrical structure and the texts associated with similar concepts can be well clustered. The euclidean and manifold geometry is unified through a regularization framework where a regularization parameter controls their balance. Although the new approach is no longer optimal in the sense of reconstruction error in euclidean space, it has a better interpretation from manifold perspective. Moreover, like CF, our method also can be performed in RKHS which gives rise to nonlinear mappings.

Keywords: concept factorization, graphs Laplacian, manifold regularization, clustering, reproducing kernel Hilbert space