{"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/grassmannian-learning-embedding-geometry","title":"Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning","arxiv_id":"1808.02229","date":"2018-08-07","proceeding":null,"authors":["Jiayao Zhang","Guangxu Zhu","Robert W. Heath Jr.","Kaibin Huang"],"abstract":"Modern machine learning algorithms have been adopted in a range of\nsignal-processing applications spanning computer vision, natural language\nprocessing, and artificial intelligence. Many relevant problems involve\nsubspace-structured features, orthogonality constrained or low-rank constrained\nobjective functions, or subspace distances. These mathematical characteristics\nare expressed naturally using the Grassmann manifold. Unfortunately, this fact\nis not yet explored in many traditional learning algorithms. In the last few\nyears, there have been growing interests in studying Grassmann manifold to\ntackle new learning problems. Such attempts have been reassured by substantial\nperformance improvements in both classic learning and learning using deep\nneural networks. We term the former as shallow and the latter deep Grassmannian\nlearning. The aim of this paper is to introduce the emerging area of\nGrassmannian learning by surveying common mathematical problems and primary\nsolution approaches, and overviewing various applications. We hope to inspire\npractitioners in different fields to adopt the powerful tool of Grassmannian\nlearning in their research.","url_abs":"http://arxiv.org/abs/1808.02229v2","url_pdf":"http://arxiv.org/pdf/1808.02229v2.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":"grassmannian-learning-embedding-geometry","repo_url":"https://github.com/matthew-mcateer/Keras_pruning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","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=1808.02229","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}