Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 31, Issue 5, Pages 3744-3759Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090748330
Keywords
Tree-Tucker; canonical decomposition; Tucker decomposition; curse of dimensionality
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Funding
- RFBR [08-01-00115, 09-01-00565, 09-01-91332]
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For d-dimensional tensors with possibly large d > 3, an hierarchical data structure, called the Tree-Tucker format, is presented as an alternative to the canonical decomposition. It has asymptotically the same (and often even smaller) number of representation parameters and viable stability properties. The approach involves a recursive construction described by a tree with the leafs corresponding to the Tucker decompositions of three-dimensional tensors, and is based on a sequence of SVDs for the recursively obtained unfolding matrices and on the auxiliary dimensions added to the initial spatial dimensions. It is shown how this format can be applied to the problem of multidimensional convolution. Convincing numerical examples are given.
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