An optimization approach for fitting canonical tensor decompositions.

Technical Report · Sun Feb 01 04:00:00 EST 2009

DOI:https://doi.org/10.2172/978916· OSTI ID:978916

Dunlavy, Daniel M ^[1]; Acar, Evrim; Kolda, Tamara Gibson

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1. Sandia National Laboratories, Albuquerque, NM

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.

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 978916
• Report Number(s): SAND2009-0857
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
DATA ANALYSIS
MATRICES
OPTIMIZATION
TENSORS