{"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/unsupervised-embedding-of-hierarchical","title":"Unsupervised Embedding of Hierarchical Structure in Euclidean Space","arxiv_id":"2010.16055","date":"2020-10-30","proceeding":null,"authors":["Jinyu Zhao","Yi Hao","Cyrus Rashtchian"],"abstract":"Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many hierarchical clustering algorithms. To bridge the gap between these two areas, we consider learning a non-linear embedding of data into Euclidean space as a way to improve the hierarchical clustering produced by agglomerative algorithms. To learn the embedding, we revisit using a variational autoencoder with a Gaussian mixture prior, and we show that rescaling the latent space embedding and then applying Ward's linkage-based algorithm leads to improved results for both dendrogram purity and the Moseley-Wang cost function. Finally, we complement our empirical results with a theoretical explanation of the success of this approach. We study a synthetic model of the embedded vectors and prove that Ward's method exactly recovers the planted hierarchical clustering with high probability.","url_abs":"https://arxiv.org/abs/2010.16055v1","url_pdf":"https://arxiv.org/pdf/2010.16055v1.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":"unsupervised-embedding-of-hierarchical","repo_url":"https://github.com/EHC-nips/Unsupervised_embedding_of_hierarchical_structure_in_euclidean_space","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2010.16055","atlas_url":"https://app.syntology.ai/?focus=2010.16055","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}