Fast damped Gauss-Newton algorithm for sparse and nonnegative tensor factorization

0360026 - ÚTIA 2012 RIV US eng C - Conference Paper (international conference)
Phan, A. H. - Tichavský, Petr - Cichocki, A.
Fast damped Gauss-Newton algorithm for sparse and nonnegative tensor factorization.
Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing 2011. Piscataway: IEEE, 2011, s. 1988-1991. ISBN 978-1-4577-0539-7.
[2011 IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP 2011. Praha (CZ), 22.05.2011-27.05.2011]
R&D Projects: GA MŠMT 1M0572; GA ČR GA102/09/1278
Institutional research plan: CEZ:AV0Z10750506
Keywords : Multilinear models * canonical polyadic decomposition * nonegative tensor factorization
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2011/SI/tichavsky-fast damped gauss-newton algorithm for nonnegative matrix factorization.pdf

Alternating optimization algorithms for canonical polyadic decomposition (with/without nonnegative constraints) often accompany update rules with low computational cost, but could face problems of swamps, bottlenecks, and slow convergence. All-at-once algorithms can deal with such problems, but always demand significant temporary extra-storage, and high computational cost. In this paper, we propose an allat- once algorithmwith lowcomplexity for sparse and nonnegative tensor factorization based on the damped Gauss-Newton iteration. Especially, for low-rank approximations, the proposed algorithm avoids building up Hessians and gradients, reduces the computational cost dramatically. Moreover, we proposed selection strategies for regularization parameters. The proposed algorithm has been verified to overwhelmingly outperform “state-of-the-art” NTF algorithms for difficult benchmarks, and for real-world application such as clustering of the ORL face database.
Permanent Link: http://hdl.handle.net/11104/0197677