Latitude: A model for mixed linear-tropical matrix factorization

Abstract

Nonnegative matrix factorization (NMF) is one of the most frequently-used matrix factorization models in data analysis. A significant reason to the popularity of NMF is its interpretability and the 'parts of whole' interpretation of its components. Recently max-times, or subtropical, matrix factorization (SMF) has been introduced as an alternative model with equally useful 'winner takes it all' interpretation. In this paper we propose a new mixed linear-tropical model and a new algorithm called Latitude that combines NMF and SMF, being able to smoothly alternate between the two. In our model the data is modeled using latent factors and additional latent parameters that control whether the factors are interpreted as NMF or SMF features or as mixtures of both. We present an algorithm for our novel matrix factorization. Our experiments show that it improves over both baselines and can yield interpretable results that reveal more of the latent structure than either NMF or SMF alone.