{"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/dimal-deep-isometric-manifold-learning-using","title":"DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling","arxiv_id":"1711.06011","date":"2017-11-16","proceeding":null,"authors":["Gautam Pai","Ronen Talmon","Alex Bronstein","Ron Kimmel"],"abstract":"This paper explores a fully unsupervised deep learning approach for computing\ndistance-preserving maps that generate low-dimensional embeddings for a certain\nclass of manifolds. We use the Siamese configuration to train a neural network\nto solve the problem of least squares multidimensional scaling for generating\nmaps that approximately preserve geodesic distances. By training with only a\nfew landmarks, we show a significantly improved local and nonlocal\ngeneralization of the isometric mapping as compared to analogous non-parametric\ncounterparts. Importantly, the combination of a deep-learning framework with a\nmultidimensional scaling objective enables a numerical analysis of network\narchitectures to aid in understanding their representation power. This provides\na geometric perspective to the generalizability of deep learning.","url_abs":"http://arxiv.org/abs/1711.06011v2","url_pdf":"http://arxiv.org/pdf/1711.06011v2.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":"dimal-deep-isometric-manifold-learning-using","repo_url":"https://github.com/paigautam/DIMAL","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.06011","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}