TY - JOUR
T1 - On optimal low rank Tucker approximation for tensors
T2 - the case for an adjustable core size
AU - Chen, Bilian
AU - Li, Zhening
AU - Zhang, Shuzhong
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/8/25
Y1 - 2015/8/25
N2 - Approximating high order tensors by low Tucker-rank tensors have applications in psychometrics, chemometrics, computer vision, biomedical informatics, among others. Traditionally, solution methods for finding a low Tucker-rank approximation presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in many applications. In this paper we propose a new computational model where the configuration and the size of the core become a part of the decisions to be optimized. Our approach is based on the so-called maximum block improvement method for non-convex block optimization. Numerical tests on various real data sets from gene expression analysis and image compression are reported, which show promising performances of the proposed algorithms.
AB - Approximating high order tensors by low Tucker-rank tensors have applications in psychometrics, chemometrics, computer vision, biomedical informatics, among others. Traditionally, solution methods for finding a low Tucker-rank approximation presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in many applications. In this paper we propose a new computational model where the configuration and the size of the core become a part of the decisions to be optimized. Our approach is based on the so-called maximum block improvement method for non-convex block optimization. Numerical tests on various real data sets from gene expression analysis and image compression are reported, which show promising performances of the proposed algorithms.
KW - Low-rank approximation
KW - Maximum block improvement
KW - Multiway array
KW - Tucker decomposition
UR - http://www.scopus.com/inward/record.url?scp=84937973588&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84937973588&partnerID=8YFLogxK
U2 - 10.1007/s10898-014-0231-x
DO - 10.1007/s10898-014-0231-x
M3 - Article
AN - SCOPUS:84937973588
SN - 0925-5001
VL - 62
SP - 811
EP - 832
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 4
ER -