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Clustering in Markov Chains with Subdominant Eigenvalues Close to One Breen, Jane
Description
Finite, discrete, time-homogeneous Markov chains are frequently used as a simple mathematical model of real-world dynamical systems. In many such applications, an analysis of clustering behaviour is desirable, and it is well-known that the eigendecomposition of the transition matrix $T$ of the chain can provide such insight. In a recent paper (see [1]), a method is presented for determining clusters from a subdominant real eigenvalue $\lambda$ of $T$ which is close to the spectral radius 1. In this talk, we extend the method to include an analysis for complex eigenvalues of $T$ which are close to 1. Since a real spectrum is not guaranteed in most applications, this is a valuable result in the area of spectral clustering in Markov chains. This is joint work with Emanuele Crisostomi, Mahsa Faizrahnemoon, Steve Kirkland, and Robert Shorten. [1] Emanuele Crisostomi, Stephen Kirkland, and Robert Shorten. A Google-like model of road network dynamics and its application to regulation and control. $\textit{International Journal of Control}$, 84(3):633--651, 2011.
Item Metadata
Title |
Clustering in Markov Chains with Subdominant Eigenvalues Close to One
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-07-08T11:01
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Description |
Finite, discrete, time-homogeneous Markov chains are frequently used as a simple mathematical model of real-world dynamical systems. In many such applications, an analysis of clustering behaviour is desirable, and it is well-known that the eigendecomposition of the transition matrix $T$ of the chain can provide such insight. In a recent paper (see [1]), a method is presented for determining clusters from a subdominant real eigenvalue $\lambda$ of $T$ which is close to the spectral radius 1. In this talk, we extend the method to include an analysis for complex eigenvalues of $T$ which are close to 1. Since a real spectrum is not guaranteed in most applications, this is a valuable result in the area of spectral clustering in Markov chains.
This is joint work with Emanuele Crisostomi, Mahsa Faizrahnemoon, Steve Kirkland, and Robert Shorten.
[1] Emanuele Crisostomi, Stephen Kirkland, and Robert Shorten. A Google-like model of road network dynamics and its application to regulation and control. $\textit{International Journal of Control}$, 84(3):633--651, 2011.
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Extent |
30 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Manitoba
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Series | |
Date Available |
2018-01-04
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0362588
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International