Publication 2010 Issue No. 8 - August Abstract - Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks
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Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks
August 2010 (vol. 32 no. 8)
pp. 1377-1391
 ASCII Text x Dan Kushnir, Meirav Galun, Achi Brandt, "Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 8, pp. 1377-1391, August, 2010.
 BibTex x @article{ 10.1109/TPAMI.2009.147,author = {Dan Kushnir and Meirav Galun and Achi Brandt},title = {Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {32},number = {8},issn = {0162-8828},year = {2010},pages = {1377-1391},doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2009.147},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - Efficient Multilevel Eigensolvers with Applications to Data Analysis TasksIS - 8SN - 0162-8828SP1377EP1391EPD - 1377-1391A1 - Dan Kushnir, A1 - Meirav Galun, A1 - Achi Brandt, PY - 2010KW - Eigenvalues and eigenvectorsKW - multigrid and multilevel methodsKW - graph algorithmsKW - segmentationKW - clustering.VL - 32JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -
Dan Kushnir, Yale University, New Haven
Meirav Galun, Weizmann Institute of Science, Rehovot
Achi Brandt, Weizmann Institute of Science, Rehovot
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.

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Index Terms:
Eigenvalues and eigenvectors, multigrid and multilevel methods, graph algorithms, segmentation, clustering.
Citation:
Dan Kushnir, Meirav Galun, Achi Brandt, "Efficient Multilevel Eigensolvers with Applications to Data Analysis Tasks," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 8, pp. 1377-1391, Aug. 2010, doi:10.1109/TPAMI.2009.147