arXiv:2410.01778v3 Announce Type: replace 
Abstract: Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting interpretability and practical visualization.
  In this work, we introduce Topological Evolution Rate (TopER), a novel, low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures, resulting in intuitive and interpretable visualizations of graph data. This approach not only enhances the exploration of graph datasets but also delivers competitive performance in graph clustering and classification tasks. Our TopER-based models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.

تم تقديم نهج جديد لتعلم تمثيل الرسوم البيانية، يُدعى معدل التطور الطوبولوجي (TopER)، والذي يبسط استخدام التماثل المستمر لإنشاء تمثيلات منخفضة الأبعاد. تُحسن هذه الطريقة من قابلية التفسير والتصور للبيانات الهيكلية في الرسوم البيانية، محققة أداءً تنافسياً في مهام التجميع والتصنيف عبر مجموعات بيانات متنوعة، بما في ذلك البيانات الجزيئية والبيولوجية والشبكات الاجتماعية.

Se ha introducido un nuevo enfoque para el aprendizaje de la representación de grafos, denominado Tasa de Evolución Topológica (TopER), que simplifica el uso de la Homología Persistente para crear embeddings de baja dimensión. Este método mejora la interpretabilidad y visualización de datos estructurados en grafos, logrando un rendimiento competitivo en tareas de agrupamiento y clasificación en diversos conjuntos de datos, incluidos los moleculares, biológicos y de redes sociales.

Une nouvelle approche de l'apprentissage de la représentation des graphes, appelée Taux d'Évolution Topologique (TopER), a été introduite, simplifiant l'utilisation de l'Homologie Persistante pour créer des embeddings de faible dimension. Cette méthode améliore l'interprétabilité et la visualisation des données structurées en graphes, atteignant des performances compétitives dans les tâches de clustering et de classification sur divers ensembles de données, y compris des réseaux moléculaires, biologiques et sociaux.

A new approach to graph representation learning, called Topological Evolution Rate (TopER), has been introduced, which simplifies the use of Persistent Homology to create low-dimensional embeddings. This method enhances the interpretability and visualization of graph-structured data, achieving competitive performance in clustering and classification tasks across various datasets, including molecular, biological, and social networks.

TopER: Topological Embeddings in Graph Representation Learning

arXiv:2506.06571v2 Announce Type: replace-cross 
Abstract: Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are increasingly employed for graph representation learning. In this context, recent works have proposed decorating classical PH diagrams with vertex and edge features for improved expressivity. However, these methods still fail to capture basic graph structural information. In this paper, we propose SpectRe -- a new topological descriptor for graphs that integrates spectral information into PH diagrams. Notably, SpectRe is strictly more expressive than existing descriptors on graphs. We also introduce notions of global and local stability to analyze existing descriptors and establish that SpectRe is locally stable. Finally, experiments on synthetic and real-world datasets demonstrate the effectiveness of SpectRe and its potential to enhance the capabilities of graph models in relevant learning tasks. Code is available at https://github.com/Aalto-QuML/SpectRe/.

تم تقديم وصف طوبولوجي جديد للرسوم البيانية، يسمى SpectRe، لتعزيز قدرة الشبكات العصبية الرسومية (GNN) من خلال دمج المعلومات الطيفية في مخططات التجانس الدائم. تهدف هذه التطورات إلى معالجة القيود التي تواجهها الطرق الحالية التي تفشل في التقاط المعلومات الهيكلية الأساسية للرسوم البيانية.

Se ha introducido un nuevo descriptor topológico para grafos, llamado SpectRe, que mejora la expresividad de las redes neuronales gráficas (GNN) al integrar información espectral en los diagramas de homología persistente. Este avance busca abordar las limitaciones de los métodos existentes que no logran capturar información estructural esencial de los grafos.

Un nouveau descripteur topologique pour les graphes, nommé SpectRe, a été introduit pour améliorer l'expressivité des réseaux de neurones graphiques (GNN) en intégrant des informations spectrales dans les diagrammes d'homologie persistante. Cette avancée vise à remédier aux limitations des méthodes existantes qui ne parviennent pas à capturer des informations structurelles essentielles des graphes.

A new topological descriptor for graphs, named SpectRe, has been introduced to enhance the expressivity of graph neural networks (GNNs) by integrating spectral information into persistent homology diagrams. This advancement aims to address the limitations of existing methods that fail to capture essential graph structural information.

TopER: Topological Embeddings in Graph Representation Learning

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