{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/geometric-laplacian-eigenmap-embedding","title":"GLEE: Geometric Laplacian Eigenmap Embedding","arxiv_id":"1905.09763","date":"2019-05-23","proceeding":null,"authors":["Leo Torres","Kevin S. Chan","Tina Eliassi-Rad"],"abstract":"Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding based on the spectral properties of the Laplacian matrix of G. 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 (or GLEE for short), and demonstrate that it outperforms various other techniques (including Laplacian Eigenmaps) in the tasks of graph reconstruction and link prediction.","url_abs":"https://arxiv.org/abs/1905.09763v2","url_pdf":"https://arxiv.org/pdf/1905.09763v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"geometric-laplacian-eigenmap-embedding","repo_url":"https://github.com/leotrs/glee","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"geometric-laplacian-eigenmap-embedding","repo_url":"https://github.com/benedekrozemberczki/karateclub","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"geometric-laplacian-eigenmap-embedding","repo_url":"https://github.com/charlie-xiao/embedding-visualization-test","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"graph-reconstruction","task_name":"Graph Reconstruction"},{"task_slug":"link-prediction","task_name":"Link Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}