TY - GEN

T1 - Under-Determined tensor diagonalization for decomposition of difficult tensors

AU - Tichavský, Petr

AU - Phan, Anh Huy

AU - Cichocki, Andrzej

PY - 2018/3/9

Y1 - 2018/3/9

N2 - Analysis of multidimensional arrays, usually called tensors, often becomes difficult in cases when the tensor rank (a minimum number of rank-one components) exceeds all the tensor dimensions. Traditional methods of canonical polyadic decomposition of such tensors, namely the alternating least squares, can be used, but a presence of a large number of false local minima can make the problem hard. Usually, multiple random initializations are advised in such cases, but the question is how many such random initializations are sufficient to get a good chance of finding the right solution. It appears that the number of the initializations can be very large. We propose a novel approach to the problem. The given tensor is augmented by some unknown parameters to the shape that admits ordinary tensor diagonalization, i.e., transforming the augmented tensor into an exact or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices. Three possible constraints are proposed to make the optimization problem well defined. The method can be modified for an under-determined block-term decomposition.

AB - Analysis of multidimensional arrays, usually called tensors, often becomes difficult in cases when the tensor rank (a minimum number of rank-one components) exceeds all the tensor dimensions. Traditional methods of canonical polyadic decomposition of such tensors, namely the alternating least squares, can be used, but a presence of a large number of false local minima can make the problem hard. Usually, multiple random initializations are advised in such cases, but the question is how many such random initializations are sufficient to get a good chance of finding the right solution. It appears that the number of the initializations can be very large. We propose a novel approach to the problem. The given tensor is augmented by some unknown parameters to the shape that admits ordinary tensor diagonalization, i.e., transforming the augmented tensor into an exact or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices. Three possible constraints are proposed to make the optimization problem well defined. The method can be modified for an under-determined block-term decomposition.

UR - http://www.scopus.com/inward/record.url?scp=85051123821&partnerID=8YFLogxK

U2 - 10.1109/CAMSAP.2017.8313082

DO - 10.1109/CAMSAP.2017.8313082

M3 - Conference contribution

AN - SCOPUS:85051123821

T3 - 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017

SP - 1

EP - 4

BT - 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017

Y2 - 10 December 2017 through 13 December 2017

ER -