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Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification

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  • Susanna Röblitz
  • Marcus Weber

Abstract

Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster Analysis (PCCA+), which delivers a fuzzy clustering. Originally developed for clustering the state space of Markov chains, the method became popular as a versatile tool for general data classification problems. The robustness of PCCA+, however, cannot be explained by previous perturbation results, because the matrices in typical applications do not comply with the two main requirements: reversibility and nearly decomposability. We therefore demonstrate in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Susanna Röblitz & Marcus Weber, 2013. "Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(2), pages 147-179, June.
    • Handle: RePEc:spr:advdac:v:7:y:2013:i:2:p:147-179
    DOI: 10.1007/s11634-013-0134-6
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    6. Lin, Yanwen & Hao, Yongchao & Shi, Qiao & Xu, Yihua & Song, Zixuan & Zhou, Ziyue & Fu, Yuequn & Zhang, Zhisen & Wu, Jianyang, 2024. "Enhanced formation of methane hydrates via graphene oxide: Machine learning insights from molecular dynamics simulations," Energy, Elsevier, vol. 289(C).
    7. Yuxuan Zhuang & Rebecca J. Howard & Erik Lindahl, 2024. "Symmetry-adapted Markov state models of closing, opening, and desensitizing in α 7 nicotinic acetylcholine receptors," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    8. Ravi Kumar Verma & Ara M Abramyan & Mayako Michino & R Benjamin Free & David R Sibley & Jonathan A Javitch & J Robert Lane & Lei Shi, 2018. "The E2.65A mutation disrupts dynamic binding poses of SB269652 at the dopamine D2 and D3 receptors," PLOS Computational Biology, Public Library of Science, vol. 14(1), pages 1-18, January.

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