Fast Similarity Computation in Factorized Tensors

  • Michael E. Houle
  • Hisashi Kashima
  • Michael Nett
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7404)


Low-rank factorizations of higher-order tensors have become an invaluable tool for researchers from many scientific disciplines. Tensor factorizations have been successfully applied for moderately sized multimodal data sets involving a small number of modes. However, a significant hindrance to the full realization of the potential of tensor methods is a lack of scalability on the client side: even when low-rank representations are provided by an external agent possessing the necessary computational resources, client applications are quickly rendered infeasible by the space requirements for explicitly storing a (dense) low-rank representation of the input tensor. We consider the problem of efficiently computing common similarity measures between entities expressed by fibers (vectors) or slices (matrices) within a given factorized tensor. We show that after appropriate preprocessing, inner products can be efficiently computed independently of the dimensions of the input tensor.


similarity computation inner products tensor factorization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael E. Houle
    • 1
  • Hisashi Kashima
    • 2
    • 3
  • Michael Nett
    • 1
    • 2
  1. 1.National Institute of InformaticsTokyoJapan
  2. 2.University of TokyoTokyoJapan
  3. 3.Basic Research Programs PRESTOSynthesis of Knowledge for Information Oriented SocietyJapan

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