Clusters in Markov chains via singular vectors of Laplacian matrices

被引：0

作者：

Cole, Sam ^{[1
]}

Kirkland, Steve ^{[2
]}

机构：

[1] NielsenIQ, Chicago, IL 60606 USA

[2] Univ Manitoba, Dept Math, Winnipeg, MB, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 660卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Markov chain; Stochastic matrix; Cluster; Left singular vector; Laplacian matrix; Contents; ALGORITHM; SUBSPACE; STATES;

D O I：

10.1016/j.laa.2022.11.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose that T is a stochastic matrix. We propose an algo-rithm for identifying clusters in the Markov chain associated with T. The algorithm is recursive in nature, and in order to identify clusters, it uses the sign pattern of a left singular vec-tor associated with the second smallest singular value of the Laplacian matrix I-T. We prove a number of results that jus-tify the algorithm's approach, and illustrate the algorithm's performance with several numerical examples.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：1 / 39

页数：39

共 39 条

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