Latitude: A model for mixed linear-tropical matrix factorization

Sanjar Karaev, James Hook, Pauli Miettinen

Research output: Contribution to conferencePaperpeer-review

3 Citations (SciVal)


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.

Original languageEnglish
Number of pages9
Publication statusPublished - 5 May 2018
Event2018 SIAM International Conference on Data Mining, SDM 2018 - San Diego, USA United States
Duration: 3 May 20185 May 2018


Conference2018 SIAM International Conference on Data Mining, SDM 2018
Country/TerritoryUSA United States
CitySan Diego


  • Matrix factorization
  • NMF
  • Subtropical algebra

ASJC Scopus subject areas

  • Computer Science Applications
  • Software


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