Parallel Nonnegative Matrix Factorization (NMF) and its Applications

A lecture entitled “Parallel Nonnegative Matrix Factorization (NMF) and its Applications” will take place on Jun. 6 at 10:00. Prof. Marian Vajtersic will present the usage of the NMF method for image reconstruction and methods of parallelization of NMF that help to speedup this reconstruction. The lecture will be held in the room TH:A-1435.

Abstract

Nonnegative matrices arise naturally in various applications. These include text mining, document classification, clustering, spectral data analysis, face recognition, and also problems in non-informatics areas, like, e.g., in computational biology. The Nonnegative Matrix Factorization (NMF) is a method for computation of a decomposition of such matrices into a product of two matrices of a smaller rank. In contrast to other techniques such as Singular Value Decomposition (SVD) or Principal Component Analysis (PCA), NMF has the distinguishing property that the factors are guaranteed to be nonnegative, which allows to interpret the factorization as an additive combination of features.

In our presentation, we show the application of NMF for image reconstruction. It will be demonstrated how the quality of the reconstruction depends on the factorization parameter and what computational and memory costs are related to it. Since processing large matrices directly can be prohibitively costly, the time needed to approximate large matrices can be decreased by using parallel computer systems.

Unfortunately, there is little related work until now on parallel distributed NMF. Therefore, we report on our parallelizations for NMF that are based on Newton-like methods.

In comparison to other algorithms to calculate the NMF, this type of methods can be parallelized very well because Newton iterations can be performed in parallel without exchanging data between processes. It was adapted for parallel execution on computer clusters, utilizing the message passing communication paradigm. Results of multiple experiments that were run on a system with up to 80 processor cores will be presented. As input matrices, images were used, which makes it possible to get a visual impression of the NMF approximation quality. The measurements show that for sufficiently large workloads, the parallelized Newton iteration algorithm achieves an almost linear speedup, which makes it a promising candidate for large-scale NMF computations.

About the Event

The event is free of charge and you do not have to register anywhere. The lecture is intended for academicians, students or researchers interested in parallel and distributed computing, numerical methods, and image processing.

Event type
Lecture
Lecturer
Prof. Marian Vajteršic
Department of Computer Sciences, Paris Lodron University of Salzburg, Austria
Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovakia
Date
June 6, 2018, 10:00
Place
Conference room TH:A-1435, Building A
Thákurova 7, Prague 6
Language
English
Video
will be not recorded

About the Lecturer

Professor Marian Vajtersic received his Ph.D. from Slovak Academy of Sciences in Bratislava in 1984. In 1994 he received the DrSc degree from the Comenius University in Bratislava. He got a habilitation in Parallel Computing from the University of Salzburg in 1996. From 2002 he is Full Professor for Computer Architecture and High-Performance Computing at this university. He is author of four monographs and more than 130 scientific papers in the area of parallel algorithms and scientific computing.

Related Content

People
Lecturer: Marian Vajteršic
Places
TH:A-1435
Person responsible for the content of this page
prof. Ing. Pavel Tvrdík, CSc., pavel.tvrdik@fit.cvut.czHead of the Department of Computer Systems


Last modified: 30.5.2018, 12:39