BigDataFr recommends: Computing Dense Tensor Decompositions with Optimal Dimension Trees

Abstract

[…] Dense tensor decompositions have been widely used in many signal processing problems including analyzing speech signals, identifying the localization of signal sources, and many other communication applications. Computing these decompositions poses major computational challenges for big datasets emerging in these domains. CANDECOMP/PARAFAC (CP) and Tucker formulations are the prominent tensor decomposition schemes heavily used in these fields, and the algorithms for computing them involve applying two core operations, namely tensor-times-matrix (TTM) and -vector (TTV) multiplication, which are executed repetitively within an iterative framework. In the recent past, efficient computational schemes using a data structure called dimension tree are employed to significantly reduce the cost of these two operations through storing and reusing partial results that are commonly used across different iterations of these algorithms.
This framework has been introduced for sparse CP and Tucker decompositions in the literature, and a recent work investigates using an optimal binary dimension tree structure in computing dense Tucker decompositions. In this pa er, we investigate finding an optimal dimension tree for both CP and Tucker decompositions. […]

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By Oguz Kaya ^1,2 Yves Robert ^1,3,2, Bora Uçar ^1,2
Source: hal-archives-ouvertes.fr

1 ROMA – Optimisation des ressources : modèles, algorithmes et ordonnancement
Inria Grenoble – Rhône-Alpes, LIP – Laboratoire de l’Informatique du Parallélisme
2 LIP – Laboratoire de l’Informatique du Parallélisme
3 The University of Tennessee [Knoxville]