Robust Ensemble Manifold Projective Non-Negative Matrix Factorization for Image Representation

Projective non-negative matrix factorization (PNMF) as a variant of NMF has received considerable attention. However, the existing PNMF methods can be further improved from two aspects. On the one hand, the square loss function that is intended to measure the reconstruction error is sensitive to noise. On the other hand, it is non-trivial to estimate the intrinsic manifold of the feature space in a principal manner. So current paper is an attempt that has proposed a new method named as robust ensemble manifold projective non-negative matrix factorization (REPNMF) for image representation. Specifically, REPNMF not only assesses the influence of noise by imposing a spare noise matrix for image reconstruction, but it also assumes that the intrinsic manifold exists in a convex hull of certain pre-given manifold candidates. We aim to remove noise from the data and find the optimized combination of candidate manifolds to approximate the intrinsic manifold simultaneously. We develop iterative multiplicative updating rules for the optimization of REPNMF along with its convergence proof. The experimental results on four image datasets verify that REPNMF is superior as compare to other related state-of-the-art methods.