2,167 research outputs found
An \~{O} Time Matrix Multiplication Algorithm
We show, for the input vectors and , where 's and 's are real numbers, after \~{O}
time preprocessing for each of them, the vector multiplication can be computed in \~{O} time. This
enables the matrix multiplication of two matrices to be computed in
\~{O} time.Comment: Version 11 and Version 12 section 2 laid the foundation of this
algorithm but has a problem unresolved. This version corrects the problem in
Version 11 and Section 2 of Version 1
Stochastic Block Coordinate Frank-Wolfe Algorithm for Large-Scale Biological Network Alignment
With increasingly "big" data available in biomedical research, deriving
accurate and reproducible biology knowledge from such big data imposes enormous
computational challenges. In this paper, motivated by recently developed
stochastic block coordinate algorithms, we propose a highly scalable randomized
block coordinate Frank-Wolfe algorithm for convex optimization with general
compact convex constraints, which has diverse applications in analyzing
biomedical data for better understanding cellular and disease mechanisms. We
focus on implementing the derived stochastic block coordinate algorithm to
align protein-protein interaction networks for identifying conserved functional
pathways based on the IsoRank framework. Our derived stochastic block
coordinate Frank-Wolfe (SBCFW) algorithm has the convergence guarantee and
naturally leads to the decreased computational cost (time and space) for each
iteration. Our experiments for querying conserved functional protein complexes
in yeast networks confirm the effectiveness of this technique for analyzing
large-scale biological networks
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