[2204.03362] The seriation problem in the presence of a double Fiedler value
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Mathematics > Numerical Analysis

arXiv:2204.03362 (math)
[Submitted on 7 Apr 2022]

Title:The seriation problem in the presence of a double Fiedler value

Authors:Anna Concas, Caterina Fenu, Giuseppe Rodriguez, Raf Vandebril
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Abstract:Seriation is a problem consisting of seeking the best enumeration order of a set of units whose interrelationship is described by a bipartite graph, that is, a graph whose nodes are partitioned in two sets and arcs only connect nodes in different groups. An algorithm for spectral seriation based on the use of the Fiedler vector of the Laplacian matrix associated to the problem was developed by Atkins et al., under the assumption that the Fiedler value is simple. In this paper, we analyze the case in which the Fiedler value of the Laplacian is not simple, discuss its effect on the set of the admissible solutions, and study possible approaches to actually perform the computation. Examples and numerical experiments illustrate the effectiveness of the proposed methods.
Comments: 24 pages, 5 figures, 3 tables
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F15, 65F50, 05C82, 91D30
Cite as: arXiv:2204.03362 [math.NA]
  (or arXiv:2204.03362v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2204.03362

Submission history

From: Caterina Fenu [view email]
[v1] Thu, 7 Apr 2022 11:02:01 UTC (54 KB)
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