Geodesic
A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 296-306
A spectral method for identifying lumping in large Markov chains is presented. The identification of meta stable states is treated as a special case. The method is based on the spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.
Classification : 15A18, 15A51, 60J10, 65F15
Keywords: Markov chain, stochastic matrix, metastable states, lumping, aggregation, modularity, block diagonal dominance, block stochastic 
@article{ETNA_2010__37__a7,
     author = {Jacobi,  Martin Nilsson},
     title = {A robust spectral method for finding lumpings and meta stable states of non-reversible {Markov} chains},
     journal = {Electronic transactions on numerical analysis},
     pages = {296--306},
     year = {2010},
     volume = {37},
     zbl = {1206.15009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a7/}
}
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VL  - 37
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%0 Journal Article
%A Jacobi,  Martin Nilsson
%T A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains
%J Electronic transactions on numerical analysis
%D 2010
%P 296-306
%V 37
%U http://geodesic.mathdoc.fr/item/ETNA_2010__37__a7/
%G en
%F ETNA_2010__37__a7
Jacobi,  Martin Nilsson. A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 296-306. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a7/