Sublinear time orthogonal tensor decomposition

Zhao Song, David P. Woodruff, Huan Zhang

Research output: Contribution to journalConference articlepeer-review


A recent work (Wang et. al., NIPS 2015) gives the fastest known algorithms for orthogonal tensor decomposition with provable guarantees. Their algorithm is based on computing sketches of the input tensor, which requires reading the entire input. We show in a number of cases one can achieve the same theoretical guarantees in sublinear time, i.e., even without reading most of the input tensor. Instead of using sketches to estimate inner products in tensor decomposition algorithms, we use importance sampling. To achieve sublinear time, we need to know the norms of tensor slices, and we show how to do this in a number of important cases. For symmetric tensors T = Σki=1 λiui⊗p with λi > 0 for all i, we estimate such norms in sublinear time whenever p is even. For the important case of p = 3 and small values of k, we can also estimate such norms. For asymmetric tensors sublinear time is not possible in general, but we show if the tensor slice norms are just slightly below || T ||F then sublinear time is again possible. One of the main strengths of our work is empirical - in a number of cases our algorithm is orders of magnitude faster than existing methods with the same accuracy.

Original languageEnglish (US)
Pages (from-to)793-801
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - 2016
Externally publishedYes
Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
Duration: Dec 5 2016Dec 10 2016

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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