Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897720 | Linear Algebra and its Applications | 2018 | 24 Pages |
Abstract
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 in the states of the system is desirable, and it is well-known that the eigendecomposition of the transition matrix A of the Markov chain can provide such insight. Clustering methods based on the sign pattern in the second eigenvector of A are frequently used when A has dominant eigenvalues that are real. In this paper, we present a method to include an analysis for complex eigenvalues of A 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jane Breen, Emanuele Crisostomi, Mahsa Faizrahnemoon, Steve Kirkland, Robert Shorten,