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On optimal low rank Tucker approximation for tensors: the case for an adjustable core size

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  • Bilian Chen
  • Zhening Li
  • Shuzhong Zhang

Abstract

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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Bilian Chen & Zhening Li & Shuzhong Zhang, 2015. "On optimal low rank Tucker approximation for tensors: the case for an adjustable core size," Journal of Global Optimization, Springer, vol. 62(4), pages 811-832, August.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:811-832
    DOI: 10.1007/s10898-014-0231-x
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    References listed on IDEAS

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