Graph regularized multilayer concept factorization for data representation

Previous studies have demonstrated that matrix factorization techniques, such as Nonnegative Matrix Factorization (NMF) and Concept Factorization (CF), have yielded impressive results in image processing and data representation. However, conventional CF and its variants with single layer factorization fail to capture the intrinsic structure of data. In this paper, we propose a novel sequential factorization method, namely Graph regularized Multilayer Concept Factorization (GMCF) for clustering. GMCF is a multi-stage procedure, which decomposes the observation matrix iteratively in a number of layers. In addition, GMCF further incorporates graph Laplacian regularization in each layer to efficiently preserve the manifold structure of data. An efficient iterative updating scheme is developed for optimizing GMCF. The convergence of this algorithm is strictly proved; the computational complexity is detailedly analyzed. Extensive experiments demonstrate that GMCF owns the superiorities in terms of data representation and clustering performance.