B1003
Title: Nonnegative matrix factorization with induced sparsity on inverse covariance matrix
Authors: Filippo Michelis - Sant\'Anna School of Advanced Studies (Italy) [presenting]
Abstract: Nonnegative matrix factorization (NMF) has become increasingly popular as a powerful method for clustering and latent factor modeling. It decomposes data into a combination of latent fundamental parts, making it effective for dimensionality reduction. Previous research has primarily focused on obtaining meaningful parts, by manifold regularization, sparseness constraints, or orthogonality, without ever modeling co-occurrence patterns directly. A new NMF method is presented that achieves meaningful parts considering how they co-occur. Attention is shifted to the relationships within parts by modeling the conditional independence relationships among them. To accomplish this, a novel regularization term is proposed that induces sparsity on the inverse covariance matrix of the latent factors. The method performance is assessed through extensive simulations and a real data case study.
