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2004

Hierarchical Eigensolver for Transition Matrices in Spectral Methods

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Hierarchical Eigensolver for Transition Matrices in Spectral Methods
We show how to build hierarchical, reduced-rank representation for large stochastic matrices and use this representation to design an efficient algorithm for computing the largest eigenvalues, and the corresponding eigenvectors. In particular, the eigen problem is first solved at the coarsest level of the representation. The approximate eigen solution is then interpolated over successive levels of the hierarchy. A small number of power iterations are employed at each stage to correct the eigen solution. The typical speedups obtained by a Matlab implementation of our fast eigensolver over a standard sparse matrix eigensolver [13] are at least a factor of ten for large image sizes. The hierarchical representation has proven to be effective in a min-cut based segmentation algorithm that we proposed recently [8]. 1 Spectral Methods Graph-theoretic spectral methods have gained popularity in a variety of application domains: segmenting images [22]; embedding in low-dimensional spaces [4, 5,...
Chakra Chennubhotla, Allan D. Jepson
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where NIPS
Authors Chakra Chennubhotla, Allan D. Jepson
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