Fast and Efficient Algorithms for Nonnegative Tucker Decomposition

  • Anh Huy Phan
  • Andrzej Cichocki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5264)


In this paper, we propose new and efficient algorithms for nonnegative Tucker decomposition (NTD): Fast α-NTD algorithm which is much precise and faster than α-NTD [1]; and β-NTD algorithm based on the β divergence. These new algorithms include efficient normalization and initialization steps which help to reduce considerably the running time and increase dramatically the performance. Moreover, the multilevel NTD scheme is also presented, allowing further improvements (almost perfect reconstruction). The performance was also compared to other well-known algorithms (HONMF, HOOI, ALS algorithms) for synthetic and real-world data as well.


Nonnegative Tucker decomposition (NTD) Nonnegative matrix factorization (NMF) Alpha divergence Beta divergence Hierarchical decomposition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Anh Huy Phan
    • 1
  • Andrzej Cichocki
    • 1
  1. 1.RIKEN Brain Science InstituteWako-shiJapan

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