Graph Vertex Embeddings: Distance, Regularization and Community Detection
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913317062180864 |
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| author | Nowak, Radosław Małkowski, Adam Cieślak, Daniel Sokół, Piotr Wawrzyński, Paweł |
| author_facet | Nowak, Radosław Małkowski, Adam Cieślak, Daniel Sokół, Piotr Wawrzyński, Paweł |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph Vertex Embeddings: Distance, Regularization and Community Detection Nowak, Radosław Małkowski, Adam Cieślak, Daniel Sokół, Piotr Wawrzyński, Paweł Social and Information Networks Machine Learning I.2.6 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. |
| title | Graph Vertex Embeddings: Distance, Regularization and Community Detection |
| topic | Social and Information Networks Machine Learning I.2.6 |
| url | https://arxiv.org/abs/2404.10784 |