TY - GEN
T1 - A Moment-Based Approach for Guaranteed Tensor Decomposition
AU - Marmin, Arthur
AU - Castella, Marc
AU - Pesquet, Jean Christophe
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - This paper presents a new scheme to perform the canonical polyadic decomposition (CPD) of a symmetric tensor. We first formulate the CPD problem as a truncated moment problem, where a measure has to be recovered knowing some of its moments. The support of the measure is discrete and encodes the CPD. The support is then retrieved by solving a polynomial system. Using algebraic results, our method resorts only to classical linear algebra operations (eigenvalue method and Schur reordered factorization). This new viewpoint offers theoretical guarantees on the retrieved decomposition. Finally experimental results show the validity of our method and a better reconstruction accuracy compared to classic CPD algorithms.
AB - This paper presents a new scheme to perform the canonical polyadic decomposition (CPD) of a symmetric tensor. We first formulate the CPD problem as a truncated moment problem, where a measure has to be recovered knowing some of its moments. The support of the measure is discrete and encodes the CPD. The support is then retrieved by solving a polynomial system. Using algebraic results, our method resorts only to classical linear algebra operations (eigenvalue method and Schur reordered factorization). This new viewpoint offers theoretical guarantees on the retrieved decomposition. Finally experimental results show the validity of our method and a better reconstruction accuracy compared to classic CPD algorithms.
KW - canonical polyadic decomposition
KW - moment problem
KW - tensors
UR - https://www.scopus.com/pages/publications/85089246266
U2 - 10.1109/ICASSP40776.2020.9054186
DO - 10.1109/ICASSP40776.2020.9054186
M3 - Conference contribution
AN - SCOPUS:85089246266
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3927
EP - 3931
BT - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Y2 - 4 May 2020 through 8 May 2020
ER -