5550
2015
eng
reportzib
0
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G-PCCA: Spectral Clustering for Non-reversible Markov Chains
Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We extend this spectral clustering method also to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension, non-reversible Markov chains can be analyzed. Furthermore, the chains need not have a positive stationary distribution. And additionally to metastabilities, dominant cycles and sinks can be identified, too.
urn:nbn:de:0297-zib-55505
Marcus Weber
Konstantin Fackeldey
Konstantin Fackeldey
ZIB-Report
15-35
Numerical Mathematics
Computational Molecular Design
Fackeldey, Konstantin
Weber, Marcus
EyeTracking
Salsa-Klimm
SFB765-C2
https://opus4.kobv.de/opus4-zib/files/5550/ZR-15-35.pdf