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Simultaneous dimension reduction and clustering via the NMF-EM algorithm

Author

Listed:
  • Léna Carel

    (Expedia Group)

  • Pierre Alquier

    (RIKEN Center for Advanced Intelligence Project)

Abstract

Mixture models are among the most popular tools for clustering. However, when the dimension and the number of clusters is large, the estimation of the clusters become challenging, as well as their interpretation. Restriction on the parameters can be used to reduce the dimension. An example is given by mixture of factor analyzers for Gaussian mixtures. The extension of MFA to non-Gaussian mixtures is not straightforward. We propose a new constraint for parameters in non-Gaussian mixture model: the K components parameters are combinations of elements from a small dictionary, say H elements, with $$H \ll K$$ H ≪ K . Including a nonnegative matrix factorization (NMF) in the EM algorithm allows us to simultaneously estimate the dictionary and the parameters of the mixture. We propose the acronym NMF-EM for this algorithm, implemented in the R package nmfem. This original approach is motivated by passengers clustering from ticketing data: we apply NMF-EM to data from two Transdev public transport networks. In this case, the words are easily interpreted as typical slots in a timetable.

Suggested Citation

  • Léna Carel & Pierre Alquier, 2021. "Simultaneous dimension reduction and clustering via the NMF-EM algorithm," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 231-260, March.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:1:d:10.1007_s11634-020-00398-4
    DOI: 10.1007/s11634-020-00398-4
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    References listed on IDEAS

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