Nonnegative matrix factorization with temporal smoothness and/or spatial decorrelation constraints

Approximate nonnegative matrix factorization (NMF) is an emerging technique with a wide spectrum of potential applications in biomedical and neurophysiological data analysis. Currently, the most popular algorithms for NMF are those proposed by Lee and Seung. However, most of the existing NMF algorithms do not provide uniqueness of the solution and the factorized components are often difficult to interpret. The key open issue is to find such nonnegative components and corresponding basis vectors that have clear physical or physiological interpretations. Since temporally smooth structures are important for hidden components in many applications, here we propose two novel constraints and derive new multiplicative learning rules that allow us to estimate such components that have physiological meanings. Specifically, we present a novel and promising application of proposed NMF algorithm to early detection of Alzheimer disease using EEG recordings.