TY - GEN

T1 - Stability analysis and fast damped-gauss-newton algorithm for INDSCAL tensor decomposition

AU - Koldovsky, Zbyněk

AU - Tichavský, Petr

AU - Phan, Anh Huy

PY - 2011

Y1 - 2011

N2 - INDSCAL is a special case of the CANDECOMP-PARAFAC (CP) decomposition of three or more-way tensors, where two factor matrices are equal. This paper provides a stability analysis of INDSCAL that is done by deriving the Cramér-Rao lower bound (CRLB) on variance of an unbiased estimate of the tensor parameters from its noisy observation (the tensor plus an i.i.d. Gaussian random tensor). The existence of the bound reveals necessary conditions for the essential uniqueness of the INDSCAL decomposition. This is compared with previous results on CP. Next, analytical expressions for the inverse of the Hessian matrix, which is needed to compute the CRLB, are used in a damped Gaussian (Levenberg-Marquardt) algorithm, which gives a novel method for INDSCAL having a lower computational complexity.

AB - INDSCAL is a special case of the CANDECOMP-PARAFAC (CP) decomposition of three or more-way tensors, where two factor matrices are equal. This paper provides a stability analysis of INDSCAL that is done by deriving the Cramér-Rao lower bound (CRLB) on variance of an unbiased estimate of the tensor parameters from its noisy observation (the tensor plus an i.i.d. Gaussian random tensor). The existence of the bound reveals necessary conditions for the essential uniqueness of the INDSCAL decomposition. This is compared with previous results on CP. Next, analytical expressions for the inverse of the Hessian matrix, which is needed to compute the CRLB, are used in a damped Gaussian (Levenberg-Marquardt) algorithm, which gives a novel method for INDSCAL having a lower computational complexity.

KW - CANDECOMP

KW - Cramér-Rao lower bound

KW - INDSCAL

KW - Levenberg-Marquardt algorithm

KW - PARAFAC

KW - tensor decomposition

UR - http://www.scopus.com/inward/record.url?scp=80052197247&partnerID=8YFLogxK

U2 - 10.1109/SSP.2011.5967765

DO - 10.1109/SSP.2011.5967765

M3 - Conference contribution

AN - SCOPUS:80052197247

SN - 9781457705700

T3 - IEEE Workshop on Statistical Signal Processing Proceedings

SP - 581

EP - 584

BT - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011

T2 - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011

Y2 - 28 June 2011 through 30 June 2011

ER -