Finding imaging patterns of structural covariance via Non-Negative Matrix Factorization

Non-negative Matrix Factorization via Archetypal Analysis

Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of ‘archetypes’ with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse), a regime that is captured by the separability condition and its generalizati...

Non-negative matrix factorization

Toward Finding Latent Cities with Non-Negative Matrix Factorization

In the last decade, digital footprints have been used to cluster population activity into functional areas of cities. However, a key aspect has been overlooked: we experience our cities not only by performing activities at specific destinations, but also by moving from one place to another. In this paper, we propose to analyze and cluster the city based on how people move through it. Particular...

Recovery Guarantee of Non-negative Matrix Factorization via Alternating Updates

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and shows that assuming a generative model of the data, it provably recovers the gro...

Bayesian Non-negative Matrix Factorization

We present a Bayesian treatment of non-negative matrix factorization (NMF), based on a normal likelihood and exponential priors, and derive an efficient Gibbs sampler to approximate the posterior density of the NMF factors. On a chemical brain imaging data set, we show that this improves interpretability by providing uncertainty estimates. We discuss how the Gibbs sampler can be used for model ...