Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:B3L-C
Session:
Number:B3L-C3
Efficient and Stable Decompositions for Multidimensional Tensors
Eugene Tyrtyshnikov, Ivan Oseledets,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
Decompositions of d-dimensional tensors are crucial either in structure recovery problems and merely for a compact representation of tensors. However, the well-known decompositions have serious drawbacks: the Tucker decompositions suffer from exponential dependence on the dimensionality d while fixed-rank canonical decompositions are not stable. In this paper we present new decompositions that are stable and have the same number of representation parameters as canonical decompositions for the same tensor. Also we present a theoretical analysis of compression properties of the new approach and discuss some applications.