Breaking the curse of dimensionality, or how to use SVD in many dimensions

I. V. Oseledets, E. E. Tyrtyshnikov

Результат исследований: Вклад в журналСтатьярецензирование

287 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Страницы (с-по)3744-3759
Число страниц16
ЖурналSIAM Journal on Scientific Computing
Том31
Номер выпуска5
DOI
СостояниеОпубликовано - 2009
Опубликовано для внешнего пользованияДа

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