Multi-manifold matrix tri-factorization for text data clustering

Abstract

We propose a novel algorithm that we called Multi-Manifold Co-clustering (MMC). This algorithm considers the geometric structures of both the sample manifold and the feature manifold simultaneously. Specifically, multiple Laplacian graph regularization terms are constructed separately to take local invariance into account; the optimal intrinsic manifold is constructed by linearly combining multiple manifolds. We employ multi-manifold learning to approximate the intrinsic manifold using a subset of candidate manifolds, which better reflects the local geometrical structure by graph Laplacian. The candidate manifolds are obtained using various representative manifold-based dimensionality reduction methods. These selected methods are based on different rationales and use different metrics for data distances. Experimental results on several real world text data sets demonstrate the effectiveness of MMC.