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 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 atthis https URL
View on arXiv@article{tulchinskii2025_2503.11910, title={ RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks }, author={ Eduard Tulchinskii and Daria Voronkova and Ilya Trofimov and Evgeny Burnaev and Serguei Barannikov }, journal={arXiv preprint arXiv:2503.11910}, year={ 2025 } }