TY - GEN

T1 - Canonical polyadic decomposition

T2 - 2012 8th International Conference on Computational Intelligence and Security, CIS 2012

AU - Zhou, Guoxu

AU - He, Zhaoshui

AU - Zhang, Yu

AU - Zhao, Qibin

AU - Cichocki, Andrzej

PY - 2012

Y1 - 2012

N2 - Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions are widely applied to analyze high order data, i.e. N-way tensors. Existing CP decomposition methods use alternating least square (ALS) iterations and hence need to compute the inverse of matrices and unfold tensors frequently, which are very time consuming for large-scale data and when N is large. Fortunately, once at least one factor has been correctly estimated, all the remaining factors can be computed efficiently and uniquely by using a series of rank-one approximations. Motivated by this fact, to perform a full N-way CP decomposition, we run 3-way CP decompositions on a sub-tensor to estimate two factors first. Then the remaining factors are estimated via an efficient Khatri-Rao product recovering procedure. In this way the whole ALS iterations with respect to each mode are avoided and the efficiency can be significantly improved. Simulations show that, compared with ALS based CP decomposition methods, the proposed method is more efficient and is easier to escape from local solutions for high order tensors.

AB - Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions are widely applied to analyze high order data, i.e. N-way tensors. Existing CP decomposition methods use alternating least square (ALS) iterations and hence need to compute the inverse of matrices and unfold tensors frequently, which are very time consuming for large-scale data and when N is large. Fortunately, once at least one factor has been correctly estimated, all the remaining factors can be computed efficiently and uniquely by using a series of rank-one approximations. Motivated by this fact, to perform a full N-way CP decomposition, we run 3-way CP decompositions on a sub-tensor to estimate two factors first. Then the remaining factors are estimated via an efficient Khatri-Rao product recovering procedure. In this way the whole ALS iterations with respect to each mode are avoided and the efficiency can be significantly improved. Simulations show that, compared with ALS based CP decomposition methods, the proposed method is more efficient and is easier to escape from local solutions for high order tensors.

KW - alternating least square

KW - CP (PARAFAC) decompositions

KW - Khatri-Rao product

KW - tensor decompositions

UR - http://www.scopus.com/inward/record.url?scp=84873563787&partnerID=8YFLogxK

U2 - 10.1109/CIS.2012.94

DO - 10.1109/CIS.2012.94

M3 - Conference contribution

AN - SCOPUS:84873563787

SN - 9780769548968

T3 - Proceedings of the 2012 8th International Conference on Computational Intelligence and Security, CIS 2012

SP - 391

EP - 395

BT - Proceedings of the 2012 8th International Conference on Computational Intelligence and Security, CIS 2012

Y2 - 17 November 2012 through 18 November 2012

ER -