Jacobi, Martin Nilsson A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains. (English) Zbl 1206.15009 ETNA, Electron. Trans. Numer. Anal. 37, 296-306 (2010). 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. Cited in 3 Documents 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 Keywords:Markov chain; stochastic matrix; metastable states; lumping; aggregation; modularity; block diagonal dominance; block stochastic PDFBibTeX XMLCite \textit{M. N. Jacobi}, ETNA, Electron. Trans. Numer. Anal. 37, 296--306 (2010; Zbl 1206.15009) Full Text: arXiv EuDML EMIS