Simultaneous dimension reduction and clustering via the NMF-EM algorithm

Léna Carel and Pierre Alquier ()
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Léna Carel: Expedia Group
Pierre Alquier: RIKEN Center for Advanced Intelligence Project

Advances in Data Analysis and Classification, 2021, vol. 15, issue 1, No 11, 260 pages

Abstract: 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.

Keywords: Mixture models; Ticketing data; Matrix factorization; Reduction of dimension; EM algorithm; Clustering; Hidden variables; Primary 62H30; Secondary 62H12; 62P25; 91C20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11634-020-00398-4

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