Naslov
Recompression of Hadamard Products of Tensors in Tucker Format

Autori
Kressner, Daniel ; Periša, Lana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo

Izvornik
METT VII — 7th Workshop on Matrix Equations and Tensor Techniques / - , 2017, 9-10

Skup
7th Workshop on Matrix Equations and Tensor Techniques

Mjesto i datum
Pisa, Italija, 13.02.2017. - 14.02.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Tensors, Tucker format, Tucker decomposition, higher-order singular value decomposition (HOSVD), Hadamard products, low-rank approximation

Sažetak
The Hadamard product features prominently in tensor-based algorithms in scientific computing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithms based on low-rank tensor representations. It is therefore of interest to develop recompression techniques that mitigate the effects of this rank increase. In this work, we investigate such techniques for the case of the Tucker format, which is well suited for tensors of low order and small to moderate multilinear ranks. Fast algorithms are attained by combining iterative methods, such as the Lanczos method and randomized algorithms, with fast matrix-vector products that exploit the structure of Hadamard products. The resulting complexity reduction is particularly relevant for tensors featuring large mode sizes I and small to moderate multilinear ranks R. To implement our algorithms, we have created a new Julia library for tensors in Tucker format.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA