Adaptive Parallel Householder Bidiagonalization

Abstract

Abstract.With the increasing use of large image and video archives and high-resolution multimedia data streams in many of today's research and application areas, there is a growing need for multimedia-oriented high-performance computing. As a consequence, a need for algorithms, methodologies, and tools that can serve as support in the (automatic) parallelization of multimedia applications is rapidly emerging.This paper discusses the parallelization of Householder bidiagonalization, a matrix factorization method which is an integral part of full Singular Value Decomposition (SVD) -an important algorithm for many multimedia problems. Householder bidiagonalization is hard to parallelize efficiently because the total number of matrix elements taking part in the calculations reduces during runtime. To overcome the growing negative performance impact of load imbalances and overprovisioning of compute resources, we apply adaptive runtime techniques of periodic matrix remapping and process reduction for improved performance. Results show that our adaptive parallel execution approach provides a significant improvement in efficiency, even when applying a set of compute resources which is (initially) very large.

A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

“…Alternatively, parallelization is possible on an algorithmic level. For example, it is possible to apply independent reflections simultaneously; the bidiagonalization has been mapped to graphical processing (GPU) units [26] and to a distributed cluster [25]. Load balancing is an issue for such parallel algorithms, however, because the number of off-diagonal columns (or rows) to eliminate get successively smaller.…”