1,035 research outputs found
Matrix Factorization at Scale: a Comparison of Scientific Data Analytics in Spark and C+MPI Using Three Case Studies
We explore the trade-offs of performing linear algebra using Apache Spark,
compared to traditional C and MPI implementations on HPC platforms. Spark is
designed for data analytics on cluster computing platforms with access to local
disks and is optimized for data-parallel tasks. We examine three widely-used
and important matrix factorizations: NMF (for physical plausability), PCA (for
its ubiquity) and CX (for data interpretability). We apply these methods to
TB-sized problems in particle physics, climate modeling and bioimaging. The
data matrices are tall-and-skinny which enable the algorithms to map
conveniently into Spark's data-parallel model. We perform scaling experiments
on up to 1600 Cray XC40 nodes, describe the sources of slowdowns, and provide
tuning guidance to obtain high performance
Scalable and interpretable product recommendations via overlapping co-clustering
We consider the problem of generating interpretable recommendations by
identifying overlapping co-clusters of clients and products, based only on
positive or implicit feedback. Our approach is applicable on very large
datasets because it exhibits almost linear complexity in the input examples and
the number of co-clusters. We show, both on real industrial data and on
publicly available datasets, that the recommendation accuracy of our algorithm
is competitive to that of state-of-art matrix factorization techniques. In
addition, our technique has the advantage of offering recommendations that are
textually and visually interpretable. Finally, we examine how to implement our
technique efficiently on Graphical Processing Units (GPUs).Comment: In IEEE International Conference on Data Engineering (ICDE) 201
QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment
Previous studies have reported that common dense linear algebra operations do
not achieve speed up by using multiple geographical sites of a computational
grid. Because such operations are the building blocks of most scientific
applications, conventional supercomputers are still strongly predominant in
high-performance computing and the use of grids for speeding up large-scale
scientific problems is limited to applications exhibiting parallelism at a
higher level. We have identified two performance bottlenecks in the distributed
memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear
algebra library. First, because ScaLAPACK assumes a homogeneous communication
network, the implementations of ScaLAPACK algorithms lack locality in their
communication pattern. Second, the number of messages sent in the ScaLAPACK
algorithms is significantly greater than other algorithms that trade flops for
communication. In this paper, we present a new approach for computing a QR
factorization -- one of the main dense linear algebra kernels -- of tall and
skinny matrices in a grid computing environment that overcomes these two
bottlenecks. Our contribution is to articulate a recently proposed algorithm
(Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in
order to confine intensive communications (ScaLAPACK calls) within the
different geographical sites. An experimental study conducted on the Grid'5000
platform shows that the resulting performance increases linearly with the
number of geographical sites on large-scale problems (and is in particular
consistently higher than ScaLAPACK's).Comment: Accepted at IPDPS10. (IEEE International Parallel & Distributed
Processing Symposium 2010 in Atlanta, GA, USA.
Parallel Nonnegative Matrix Factorization Algorithms for Hyperspectral Images
Hyperspectral imaging is a branch of remote sensing which deals with creating and processing aerial or satellite pictures that capture wide range of wavelengths, most of which are invisible to the naked eye. Hyperspectral images are composed of many bands, each corresponding to certain light frequencies. Because of their complex nature, image processing tasks such as feature extraction can be resource and time consuming. There are many unsupervised extraction methods available. A recently investigated one is Nonnegative Matrix Factorization (NMF), a method that given positive linear matrix of positive sources, attempts to recover them. In this thesis we designed, implemented and tested parallel versions of two popular iterative NMF algorithms: one based on multiplicative updates, and another on alternative gradient computation.
Our algorithms are designed to leverage the multi-processor SMP architecture and power of threading to evenly distribute the workload among the available CPU’s and improve the performance as compared to their sequential counterparts. This work could be used as a basis for creating even more powerful distributed algorithms that would work on clustered architectures. The experiments show a speedup in both algorithms without reduction in accuracy.
In addition, we have also developed a java based framework offering reading and writing tools for various hyperspectral image types, as well as visualization tools, and a graphical user interface to launch and control the factorization processes
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