Section: New Results

Distributed memory tensor computations

Participants : Oguz Kaya, Bora Uçar.

There are two prominent tensor decomposition formulations. CANDECOMP/PARAFAC (CP) formulation approximates a tensor as a sum of rank-one tensors. Tucker formulation approximates a tensor with a core tensor multiplied by a matrix along each mode. Both of these formulations have uses in applications. The most common algorithms for both decompositions are based on the alternating least squares method. The algorithms of this type are iterative, where the computational core of an iteration is a special operation operation between an $N$-mode tensor and $N$ matrices. These key operations are called the matricized tensor times Khatri-Rao product (MTTKRP) in the CP-ALS case, and the $n$-mode product in the Tucker decomposition case. We have investigated efficient parallelizations of full fledged algorithms for obtaining these two decompositions in distributed memory systems [30] , [51] with a special focus on the mentioned key operations. In both studies, hypergraphs are used for computational load balancing and communication cost reduction. We are currently finalizing our last touches on the Tucker decomposition algorithms [51] to submit it to a conference. We are also working towards a unified view of the parallelization of the two algorithms. This work with its whole extend is carried out in the context of the thesis of Oguz Kaya.