RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks

• URL: http://arxiv.org/abs/2503.11910v1
• Date: Fri, 14 Mar 2025 22:42:13 GMT
• Title: RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks
• Authors: Eduard Tulchinskii, Daria Voronkova, Ilya Trofimov, Evgeny Burnaev, Serguei Barannikov,
• Abstract summary: Topological methods for comparing weighted graphs often suffer from computational inefficiency on large datasets.<n>We introduce RTD-Lite, a scalable algorithm that efficiently compares topological features.<n>This efficiency enables its application in tasks like dimensionality reduction and neural network training.
• Score: 21.49200381462702
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological methods for comparing weighted graphs are valuable in various learning tasks but often suffer from computational inefficiency on large datasets. We introduce RTD-Lite, a scalable algorithm that efficiently compares topological features, specifically connectivity or cluster structures at arbitrary scales, of two weighted graphs with one-to-one correspondence between vertices. Using minimal spanning trees in auxiliary graphs, RTD-Lite captures topological discrepancies with $O(n^2)$ time and memory complexity. This efficiency enables its application in tasks like dimensionality reduction and neural network training. Experiments on synthetic and real-world datasets demonstrate that RTD-Lite effectively identifies topological differences while significantly reducing computation time compared to existing methods. Moreover, integrating RTD-Lite into neural network training as a loss function component enhances the preservation of topological structures in learned representations. Our code is publicly available at https://github.com/ArGintum/RTD-Lite

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