Bibliography
Conference Paper (international conference)
Rank Splitting for CANDECOMP/PARAFAC
, ,
: Latent Variable Analysis and Signal Separation, p. 31-40 , Eds: Vincent Emmanuel, Yeredor Arie, Koldovský Zbyněk, Tichavský Petr
: Latent Variable Analysis and Signal Separation 12th International Conference, LVA/ICA 2015, (Liberec, CZ, 25.08.2015-28.08.2015)
: GA14-13713S, GA ČR
: Canonical polyadic decomposition, PARAFAC, deflation
: http://library.utia.cas.cz/separaty/2015/SI/tichavsky-0447197.pdf
(eng): CANDECOMP/PARAFAC (CP) approximates multiway data by a sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of rank-1 tensor components. In this paper, we extend the method to block deflation problem. When at least two factor matrices have full column rank, one can extract two rank-1 tensors simultaneously, and rank of the data tensor is reduced by 2. For decomposition of order-3 tensors of size R×R×R and rank-R, the block deflation has a complexity of O(R^3) per iteration which is lower than the cost O(R^4) of the ALS algorithm for the overall CP decomposition.
: BB