TopER: Topological Embeddings in Graph Representation Learning

Astrit Tola, Funmilola Mary Taiwo, Cuneyt Gurcan Akcora, Baris Coskunuzer

Keywords: Graph embeddings, graph classification, graph representation learning, interpretability, data visualization, topological data analysis

TL;DR: We introduce TopER, a unique low-dimensional topological embedding method that provides one of the first effective ways for visualizing graph datasets while also doing exceptionally well in graph classification tasks.

Abstract:

Graph embeddings serve as the cornerstone for graph representation learning, facilitating the exploration of graphs by machine learning methods. However, prevalent deep learning techniques rely on black-box, high-dimensional graph embeddings. There is a pressing need for an interpretable, low-dimensional embedding approach to empower efficient graph visualization and provide practical tools to study graph datasets effectively.

In this paper, we present a novel low-dimensional graph embedding method called *Topological Evolution Rate (TopER)*, which simplifies a key concept of topological data analysis known as *filtration*. TopER calculates the evolution rate of graph substructures induced by a filtration function on nodes or edges, resulting in interpretable 2D visualizations of graph datasets. Our experiments demonstrate that this new embedding method achieves highly competitive performance compared to the latest deep learning models in graph classification tasks on benchmark datasets. We further provide theoretical stability guarantees for TopER.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 3452