30,338 research outputs found
Common and Distinct Components in Data Fusion
In many areas of science multiple sets of data are collected pertaining to
the same system. Examples are food products which are characterized by
different sets of variables, bio-processes which are on-line sampled with
different instruments, or biological systems of which different genomics
measurements are obtained. Data fusion is concerned with analyzing such sets of
data simultaneously to arrive at a global view of the system under study. One
of the upcoming areas of data fusion is exploring whether the data sets have
something in common or not. This gives insight into common and distinct
variation in each data set, thereby facilitating understanding the
relationships between the data sets. Unfortunately, research on methods to
distinguish common and distinct components is fragmented, both in terminology
as well as in methods: there is no common ground which hampers comparing
methods and understanding their relative merits. This paper provides a unifying
framework for this subfield of data fusion by using rigorous arguments from
linear algebra. The most frequently used methods for distinguishing common and
distinct components are explained in this framework and some practical examples
are given of these methods in the areas of (medical) biology and food science.Comment: 50 pages, 12 figure
Summary of the functions and capabilities of the structural analysis and matrix interpretive system computer program
Functions and capabilities of large capacity structural analysis and matrix interpretive system digital computer program to analyze frame and shell structure
Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many
high-performance graph algorithms as well as for some linear solvers, such as
algebraic multigrid. The scaling of existing parallel implementations of SpGEMM
is heavily bound by communication. Even though 3D (or 2.5D) algorithms have
been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi
matrices, those algorithms had not been implemented in practice and their
complexities had not been analyzed for the general case. In this work, we
present the first ever implementation of the 3D SpGEMM formulation that also
exploits multiple (intra-node and inter-node) levels of parallelism, achieving
significant speedups over the state-of-the-art publicly available codes at all
levels of concurrencies. We extensively evaluate our implementation and
identify bottlenecks that should be subject to further research
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