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Nonnegative matrix factorization (NMF) is one of the most frequently-usedmatrix factorization models in data analysis. A significant reason to thepopularity of NMF is its interpretability and the `parts of whole'interpretation of its components. Recently, max-times, or subtropical, matrixfactorization (SMF) has been introduced as an alternative model with equallyinterpretable `winner takes it all' interpretation. In this paper we propose anew mixed linear--tropical model, and a new algorithm, called Latitude, thatcombines NMF and SMF, being able to smoothly alternate between the two. In ourmodel, the data is modeled using the latent factors and latent parameters thatcontrol whether the factors are interpreted as NMF or SMF features, or theirmixtures. We present an algorithm for our novel matrix factorization. Ourexperiments show that our algorithm improves over both baselines, and can yieldinterpretable results that reveal more of the latent structure than either NMFor SMF alone.

Latitude: A Model for Mixed Linear-Tropical Matrix Factorization