Graph Vertex Embeddings: Distance, Regularization and Community Detection

• URL: http://arxiv.org/abs/2404.10784v1
• Date: Tue, 9 Apr 2024 09:03:53 GMT
• Title: Graph Vertex Embeddings: Distance, Regularization and Community Detection
• Authors: Radosław Nowak, Adam Małkowski, Daniel Cieślak, Piotr Sokół, Paweł Wawrzyński,
• Abstract summary: Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space. We present a family of flexible distance functions that faithfully capture the topological distance between different vertices. We evaluate the effectiveness of our proposed embedding constructions by performing community detection on a host of benchmark datasets.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the topological structure of the data. In this paper, we explore several aspects that affect the quality of a vertex embedding of graph-structured data. To this effect, we first present a family of flexible distance functions that faithfully capture the topological distance between different vertices. Secondly, we analyze vertex embeddings as resulting from a fitted transformation of the distance matrix rather than as a direct result of optimization. Finally, we evaluate the effectiveness of our proposed embedding constructions by performing community detection on a host of benchmark datasets. The reported results are competitive with classical algorithms that operate on the entire graph while benefitting from a substantially reduced computational complexity due to the reduced dimensionality of the representations.

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