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.
Bibliographical noteFunding Information:
This work was partially supported by National Science Foundation of China (Grant 11301436 and 11371242), National Science Foundation of USA (Grant CMMI-1161242), Natural Science Foundation of Shanghai (Grant 12ZR1410100), and Ph.D. Programs Foundation of Chinese Ministry of Education (Grant 20123108120002). We would like to thank the anonymous referee for the insightful suggestions.
© 2014, Springer Science+Business Media New York.
- Low-rank approximation
- Maximum block improvement
- Multiway array
- Tucker decomposition