PQSER: A Matlab package for spectral seriation

TL;DR

This paper introduces PQSER, a MATLAB package implementing spectral seriation algorithms based on Fiedler vectors, with improvements for handling real-world data and multiple Fiedler values.

Contribution

It provides a practical MATLAB implementation of spectral seriation with technical enhancements and guidance for real-world applications.

Findings

Improved algorithm performance through numerical techniques.

Effective handling of multiple Fiedler values in inconsistent data.

Demonstrated applicability on real-world data sets.

Abstract

The seriation problem is an important ordering issue which consists of finding the best ordering of a set of units whose interrelationship is defined by a bipartite graph. It has important applications in, e.g., archaeology, anthropology, psychology, and biology. This paper presents a Matlab implementation of an algorithm for spectral seriation by Atkins et al., based on the use of the Fiedler vector of the Laplacian matrix associated to the problem, which encodes the set of admissible solutions into a PQ-tree. We introduce some numerical technicalities in the original algorithm to improve its performance, and point out that the presence of a multiple Fiedler value may have a substantial influence on the computation of an approximated solution, in the presence of inconsistent data sets. Practical examples and numerical experiments show how to use the toolbox to process data sets deriving from real-world applications.