# Coarse-graining and reconstruction for Markov matrices

@inproceedings{Stephan2021CoarsegrainingAR, title={Coarse-graining and reconstruction for Markov matrices}, author={Artur Stephan}, year={2021} }

We present a coarse-graining (or model order reduction) procedure for stochastic matrices by clustering. The method is consistent with the natural structure of Markov theory, preserving positivity and mass, and does not rely on any tools from Hilbert space theory. The reconstruction is provided by a generalized Penrose-Moore inverse of the coarsegraining operator incorporating the inhomogeneous invariant measure of the Markov matrix. As we show, the method provides coarse-graining and…

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