Latitude: A Model for Mixed Linear-Tropical Matrix Factorization

TL;DR

This paper introduces Latitude, a novel matrix factorization model that combines nonnegative and tropical factorizations, allowing for flexible interpretation and improved latent structure discovery.

Contribution

The paper proposes a new mixed linear-tropical matrix factorization model and an algorithm that smoothly integrates NMF and SMF, enhancing interpretability and latent structure analysis.

Findings

Latitude outperforms baseline models in experiments.

It provides more interpretable and richer latent features.

The model effectively balances between NMF and SMF interpretations.

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 interpretable `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 the latent factors and latent parameters that control whether the factors are interpreted as NMF or SMF features, or their mixtures. We present an algorithm for our novel matrix factorization. Our experiments show that our algorithm improves over both baselines, and can yield interpretable results that reveal more of the latent structure than either NMF or SMF alone.