Algorithm for Interpretable Graph Features via Motivic Persistent Cohomology

2025-12-23 · Yoshihiro Maruyama arxiv

We present the Chromatic Persistence Algorithm (CPA), an event-driven method for computing persistent cohomological features of weighted graphs via graphic arrangements, a classical object in computational geometry. We establish rigorous complexity results: CPA is exponential in the worst case, fixed-parameter tractable in treewidth, and nearly linear for common graph families such as trees, cycles, and series-parallel graphs. Finally, we demonstrate its practical applicability through a controlled experiment on molecular-like graph structures.

📄 PDF Abstract BibTeX arXiv:2512.20311

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Probabilistic Multilabel Graphical Modelling of Motif Transformations in Symbolic Music

2026-03-27 · Ron Taieb, Yoel Greenberg, Barak Sober arxiv

Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in …

Motivic clustering schemes for directed graphs

2020-01-01 · Facundo Mémoli, Guilherme Vituri F. Pinto

Motivated by the concept of network motifs we construct certain clustering methods (functors) which are parametrized by a given collection of motifs (or representers).

Clustering

TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration

2025-10-06 · Cheng Xin, Fan Xu, Xin Ding, Jie Gao 외 arxiv

Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsically interpr…

Graph Learning

Topological Methods in Machine Learning: A Tutorial for Practitioners

2024-09-04 · Baris Coskunuzer, Cüneyt Gürcan Akçora

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutoria…

Neural Approximation of Graph Topological Features

2022-01-28 · Zuoyu Yan, Tengfei Ma, Liangcai Gao, Zhi Tang 외

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large …

Graph Learning Graph Neural Network Graph Representation Learning Representation Learning+1