Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions 论文

详细信息

发表期刊/会议

SIAM Journal on Scientific Computing

发表日期

2009-01-01

发表年份

2009

摘要

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.