Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
The trace minimization method for the symmetric generalized eigenvalue problem
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Graph matching and clustering using spectral partitions
Pattern Recognition
Spectral clustering and its use in bioinformatics
Journal of Computational and Applied Mathematics
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers
SIAM Journal on Scientific Computing
Web document clustering using hyperlink structures
Computational Statistics & Data Analysis
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The eigenvector corresponding to the second smallest eigenvalue of the Laplacian of a graph, known as the Fiedler vector, has a number of applications in areas that include matrix reordering, graph partitioning, protein analysis, data mining, machine learning, and web search. The computation of the Fiedler vector has been regarded as an expensive process as it involves solving a large eigenvalue problem. We present a novel and efficient parallel algorithm for computing the Fiedler vector of large graphs based on the Trace Minimization algorithm. We compare the parallel performance of our method with a multilevel scheme, designed specifically for computing the Fiedler vector, which is implemented in routine MC73 FIEDLER of the Harwell Subroutine Library (HSL).