A scalable optimization approach for fitting canonical tensor decompositions
Article first published online: 27 JAN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Journal of Chemometrics
Volume 25, Issue 2, pages 67–86, February 2011
How to Cite
Acar, E., Dunlavy, D. M. and Kolda, T. G. (2011), A scalable optimization approach for fitting canonical tensor decompositions. J. Chemometrics, 25: 67–86. doi: 10.1002/cem.1335
- Issue published online: 22 FEB 2011
- Article first published online: 27 JAN 2011
- Manuscript Accepted: 14 JUN 2010
- Manuscript Revised: 8 JUN 2010
- Manuscript Received: 5 APR 2010
- tensor decomposition;
- tensor factorization;
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 CANDECOMP/PARAFAC (CP), 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 CP, however, can be difficult. The typical approach is based on alternating least-squares (ALS) optimization, but it is not accurate in the case of overfactoring. High accuracy can be obtained by using nonlinear least-squares (NLS) methods; the disadvantage is that NLS methods are much slower than ALS. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and 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 more accurate than ALS and faster than NLS in terms of total computation time. Copyright © 2011 John Wiley & Sons, Ltd.