Graph Vertex Embeddings: Distance, Regularization and Community Detection
<|reference_start|>Graph Vertex Embeddings: Distance, Regularization and Community Detection: 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.<|reference_end|>
@article{nowak2024graph,
    title={Graph Vertex Embeddings: Distance, Regularization and Community
  Detection},
    author={Rados{l}aw Nowak, Adam Ma{l}kowski, Daniel Cie'slak, Piotr
  Sok'o{l}, Pawe{l} Wawrzy'nski},
    journal={arXiv preprint arXiv:2404.10784},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10784},
    primaryClass={cs.SI cs.LG}
}