Papers › Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models

24 Jun 2025arXiv:2506.19821archive 2025-07-28

Víctor Blanco, Alfredo Marín, Justo Puerto

Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span clustering, anomaly detection, and beyond. In this work, we present a unified framework grounded in mathematical optimization to address matrix seriation from a rigorous, model-based perspective. Our approach leverages combinatorial and mixed-integer optimization to represent seriation objectives and constraints with high fidelity, bridging the gap between traditional heuristic methods and exact solution techniques. We introduce new mathematical programming models for neighborhood-based stress criteria, including nonlinear formulations and their linearized counterparts. For structured settings such as Moore and von Neumann neighborhoods, we develop a novel Hamiltonian path-based reformulation that enables effective control over spatial arrangement and interpretability in the reordered matrix. To assess the practical impact of our models, we carry out an extensive set of experiments on synthetic and real-world datasets, as well as on a newly curated benchmark based on a coauthorship network from the matrix seriation literature. Our results show that these optimization-based formulations not only enhance solution quality and interpretability but also provide a versatile foundation for extending matrix seriation to new domains in data science.

PaperPDFCode

Code

vblancoor/seriation_mathopt officialmentioned in paper report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Anomaly Detection

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

SET

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections