{"title":"GLEE: Geometric Laplacian Eigenmap Embedding","authors":"Leo Torres, Kevin S. Chan, Tina Eliassi-Rad","abstract":"Graph embedding seeks to build a low-dimensional representation of a graph \r\nG. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps (LE), which constructs a graph embedding based on the spectral properties of the Laplacian matrix of \r\nG. The intuition behind it, and many other embedding techniques, is that the embedding of a graph must respect node similarity: similar nodes must have embeddings that are close to one another. Here, we dispose of this distance-minimization assumption. Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of G. We introduce a new approach, Geometric Laplacian Eigenmap Embedding, and demonstrate that it outperforms various other techniques (including LE) in the tasks of graph reconstruction and link prediction.","keywords":["graph embedding","graph Laplacian","simplex geometry"],"year":2026,"slug":"glee","version":1,"url_hash":"9bf73ea5ee86","license":"cc-by-4.0","doi":"10.5281/zenodo.19110499","published_at":"2026-03-17T12:59:25.528873+00:00","subject":"Computer Science","storage_type":"inline","canonical_url":"https://scroll.press/2026/glee","version_url":"https://scroll.press/2026/glee/v1","paper_url":"https://scroll.press/2026/glee/paper","paper_version_url":"https://scroll.press/2026/glee/v1/paper","html_url":"https://scroll.press/2026/glee/paper","html_sha256":"9bf73ea5ee86d440cfd99e2efbadec6e8bbc545463e65a7697cf5bcbc3e185a6","html_bytes":1422094,"cite_as":{"bibtex":"@misc{glee2026,\n  author = {Torres, Leo and Chan, Kevin S. and Eliassi-Rad, Tina},\n  title = {GLEE: Geometric Laplacian Eigenmap Embedding},\n  year = {2026},\n  publisher = {Scroll Press},\n  url = {https://scroll.press/2026/glee},\n  version = {1},\n  doi = {10.5281/zenodo.19110499}\n}","csl_json":{"type":"article","id":"9bf73ea5ee86","title":"GLEE: Geometric Laplacian Eigenmap Embedding","author":[{"family":"Torres","given":"Leo"},{"family":"Chan","given":"Kevin S."},{"family":"Eliassi-Rad","given":"Tina"}],"publisher":"Scroll Press","URL":"https://scroll.press/2026/glee","version":"1","issued":{"date-parts":[[2026]]},"DOI":"10.5281/zenodo.19110499","license":"cc-by-4.0"}}}