Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks
Multigrid solvers proved very efficient for solving massive systems of equations in various fields. These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensol...
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| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence 2010-08, Vol.32 (8), p.1377-1391 |
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| container_title | IEEE transactions on pattern analysis and machine intelligence |
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| creator | Kushnir, Dan Galun, Meirav Brandt, Achi |
| description | Multigrid solvers proved very efficient for solving massive systems of equations in various fields. These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively. |
| doi_str_mv | 10.1109/TPAMI.2009.147 |
| format | Article |
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These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively.</description><identifier>ISSN: 0162-8828</identifier><identifier>EISSN: 1939-3539</identifier><identifier>DOI: 10.1109/TPAMI.2009.147</identifier><identifier>PMID: 20558872</identifier><identifier>CODEN: ITPIDJ</identifier><language>eng</language><publisher>Los Alamitos, CA: IEEE</publisher><subject>Algorithmics. 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These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Artificial intelligence</subject><subject>clustering</subject><subject>Clustering algorithms</subject><subject>Computational complexity</subject><subject>Computer science; control theory; systems</subject><subject>Data analysis</subject><subject>Data processing</subject><subject>Data processing. List processing. Character string processing</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Eigenvalues and eigenvectors</subject><subject>Equations</subject><subject>Exact sciences and technology</subject><subject>graph algorithms</subject><subject>Image segmentation</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Matrix decomposition</subject><subject>Memory organisation. Data processing</subject><subject>multigrid and multilevel methods</subject><subject>Multilevel</subject><subject>Pattern recognition. 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| identifier | ISSN: 0162-8828 |
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| issn | 0162-8828 1939-3539 |
| language | eng |
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| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Approximation Artificial intelligence clustering Clustering algorithms Computational complexity Computer science control theory systems Data analysis Data processing Data processing. List processing. Character string processing Eigenvalues and eigenfunctions Eigenvalues and eigenvectors Equations Exact sciences and technology graph algorithms Image segmentation Interpolation Mathematical analysis Matrix decomposition Memory organisation. Data processing multigrid and multilevel methods Multilevel Pattern recognition. Digital image processing. Computational geometry Sampling methods segmentation Software Solvers Sparse matrices Tasks Theoretical computing |
| title | Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks |
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