Session B7 - Numerical Linear Algebra
July 13, 14:30 ~ 15:00 - Room B5
Numerical optimization strategies for large-scale (constrained, coupled) matrix/tensor factorization
Lieven De Lathauwer
KU Leuven, Belgium - Lieven.DeLathauwer@kuleuven.be
We give an overview of recent developments in numerical optimization-based computation of tensor decompositions. By careful exploitation of tensor product structure in methods such as quasi-Newton and nonlinear least squares, good convergence is combined with fast computation. A modular approach extends the computation to coupled factorizations and structured factors. Compact representations (polyadic, Tucker, ...) of large data sets may be obtained by stochastic optimization, randomization, compressed sensing, ... Careful exploitation of the representation structure allows us to scale the numerical algorithms to large problem size. The discussion is illustrated with application examples.
Vervliet N., Debals O., De Lathauwer L., "Tensorlab 3.0 - Numerical optimization strategies for large-scale constrained and coupled matrix/tensor factorization", in Proc. of the 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Nov. 2016, pp. 1733-1738.
Vervliet N., Debals O., Sorber L., Van Barel M., De Lathauwer L., Tensorlab 3.0, Available online, Mar. 2016. URL: http://www.tensorlab.net/
Joint work with Nico Vervliet (KU Leuven, Belgium), Otto Debals (KU Leuven, Belgium), Laurent Sorber (KU Leuven, Belgium)(now Forespell, Belgium) and Marc Van Barel (KU Leuven, Belgium).