Variational bayesian partially observed non-negative tensor factorization

Jesper Løve Hinrich, Søren Føns Vind Nielsen, Kristoffer Hougaard Madsen, Morten Mørup

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Non-negative matrix and tensor factorization (NMF/NTF) have become important tools for extracting part based representations in data. It is however unclear when an NMF or NTF approach is most suited for data and how reliably the models predict when trained on partially observed data. We presently extend a recently proposed variational Bayesian NMF (VB-NMF) to non-negative tensor factorization (VB-NTF) for partially observed data. This admits bi- and multi-linear structure quantification considering both model prediction and evidence. We evaluate the developed VB-NTF on synthetic and a real dataset of gene expression in the human brain and contrast the performance to VB-NMF and conventional NMF/NTF. We find that the gene expressions are better accounted for by VB-NMF than VB-NTF and that VB-NMF/VB-NTF more robustly handle partially observed data than conventional NMF/NTF. In particular, probabilistic modeling is beneficial when large amounts of data is missing and/or the model order over-specified.
Original languageEnglish
Title of host publicationProceedings of 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing
Number of pages6
Publication date2018
ISBN (Print)9781538654774
Publication statusPublished - 2018
Event2018 IEEE International Workshop on Machine Learning for Signal Processing - Aalborg, Denmark
Duration: 17 Sep 201820 Sep 2018


Conference2018 IEEE International Workshop on Machine Learning for Signal Processing


  • Probabilistic modeling
  • Missing data
  • Human brain microarray data
  • Non-negative tensor factorization


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