An optimization approach for fitting canonical tensor decompositions.

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Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods ... continued below

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40 p.

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Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim & Kolda, Tamara Gibson February 1, 2009.

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Description

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.

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40 p.

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  • Report No.: SAND2009-0857
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/978916 | External Link
  • Office of Scientific & Technical Information Report Number: 978916
  • Archival Resource Key: ark:/67531/metadc930924

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  • February 1, 2009

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Nov. 30, 2016, 2:52 p.m.

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Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim & Kolda, Tamara Gibson. An optimization approach for fitting canonical tensor decompositions., report, February 1, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc930924/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.