Parallel optimization algorithms for very large tensor decompositionsParallel optimization algorithms for very large tensor decompositionsΠαράλληλοι αλγόριθμοι βελτιστοποίησης για παραγοντοποιήσεις πολύ μεγάλων τανυστών Διπλωματική Εργασία Diploma Work 2019-10-042019enTensors are generalizations of matrices to higher dimensions and are very powerful tools that can model a wide variety of multi-way data dependencies. As a result, tensor decompositions can extract useful information out of multi-aspect data tensors and have witnessed increasing popularity in various fields, such as data mining, social network analysis, biomedical applications, machine learning etc. Many decompositions have been proposed, but in this thesis we focus on Tensor Rank Decomposition or Canonical Polyadic Decomposition (CPD) using Alternating Least Squares (ALS). The main goal of the CPD is to decompose tensors into a sum of rank-1 terms, a procedure more difficult than its matrix counterpart, especially for large-scale tensors. CP decomposition via ALS consists of computationally expensive operations which cause performance bottlenecks. In order to accelerate this method and overcome these obstacles, we developed two parallel versions of the ALS that implement the CPD. The first one uses the full tensor and runs in parallel on heterogeneous & shared memory systems (CPUs and GPUs). The second one decomposes the tensor in parallel using small random block samples and runs on homogeneous & shared memory systems (CPUs).http://creativecommons.org/licenses/by/4.0/Πολυτεχνείο Κρήτης::Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών ΥπολογιστώνPapagiannakos_Ioannis-Marios_Dip_2019.pdfChania [Greece]Library of TUC2019-10-04application/pdf831.5 kBfree Papagiannakos Ioannis-Marios Παπαγιαννακος Ιωαννης-Μαριος Liavas Athanasios Λιαβας Αθανασιος Karystinos Georgios Καρυστινος Γεωργιος Samoladas Vasilis Σαμολαδας Βασιλης Πολυτεχνείο Κρήτης Technical University of Crete Canonical polyadic decomposition Alternating least squares shared memory systems OpenMP CUDA Tensor Randomized block sampling PARAFAC Parallel computing