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A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains. (English) Zbl 1206.15009

Summary: 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.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B51 Stochastic matrices
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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