Hybrid Manifold Regularized Non-negative Matrix Factorization for Data Representation

Non-negative Matrix Factorization (NMF) has received considerable attention due to its parts-based representation and interpretability of the issue correspondingly. On the other hand, data usually reside on a submanifold of the ambient space. One hopes to find a compact representation which captures the hidden semantic relationships between data items and reveals the intrinsic geometric structure simultaneously. However, it is difficult to estimate the intrinsic manifold of the data space in a principled way. In this paper, we propose a novel algorithm, called Hybrid Manifold Regularized Non-negative Matrix Factorization (HMNMF), for this purpose. In HMNMF, we develop a hybrid manifold regularization framework to approximate the intrinsic manifold by combining different initial guesses. Experiments on two real-world datasets validate the effectiveness of new method.