What Relations Are Reliably Embeddable in Euclidean Space?. Bhattacharjee, R. and Dasgupta, S.
What Relations Are Reliably Embeddable in Euclidean Space? [link]Paper  abstract   bibtex   
We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.
@article{bhattacharjeeWhatRelationsAre2019,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1903.05347},
  primaryClass = {cs, stat},
  title = {What Relations Are Reliably Embeddable in {{Euclidean}} Space?},
  url = {http://arxiv.org/abs/1903.05347},
  abstract = {We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.},
  urldate = {2019-03-14},
  date = {2019-03-13},
  keywords = {Statistics - Machine Learning,Computer Science - Machine Learning},
  author = {Bhattacharjee, Robi and Dasgupta, Sanjoy},
  file = {/home/dimitri/Nextcloud/Zotero/storage/J33WQ846/Bhattacharjee and Dasgupta - 2019 - What relations are reliably embeddable in Euclidea.pdf;/home/dimitri/Nextcloud/Zotero/storage/9KPSSFIP/1903.html}
}
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