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

Susanna Röblitz () and Marcus Weber

Advances in Data Analysis and Classification, 2013, vol. 7, issue 2, 147-179

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

Keywords: Perron eigenvalues; Perturbation theory; Molecular simulations; 60J10; 62H30; 65K05 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11634-013-0134-6 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:advdac:v:7:y:2013:i:2:p:147-179

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-013-0134-6

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from 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)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().