{"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/a-statistical-recurrent-model-on-the-manifold","title":"A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices","arxiv_id":"1805.11204","date":"2018-05-29","proceeding":"NeurIPS 2018 12","authors":["Rudrasis Chakraborty","Chun-Hao Yang","Xingjian Zhen","Monami Banerjee","Derek Archer","David Vaillancourt","Vikas Singh","Baba C. Vemuri"],"abstract":"In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed\nare non-Euclidean in nature. Geometric deep learning corresponds to techniques\nthat generalize deep neural network models to such non-Euclidean spaces.\nSeveral recent papers have shown how convolutional neural networks (CNNs) can\nbe extended to learn with graph-based data. In this work, we study the setting\nwhere the data (or measurements) are ordered, longitudinal or temporal in\nnature and live on a Riemannian manifold -- this setting is common in a variety\nof problems in statistical machine learning, vision and medical imaging. We\nshow how recurrent statistical recurrent network models can be defined in such\nspaces. We give an efficient algorithm and conduct a rigorous analysis of its\nstatistical properties. We perform extensive numerical experiments\ndemonstrating competitive performance with state of the art methods but with\nsignificantly less number of parameters. We also show applications to a\nstatistical analysis task in brain imaging, a regime where deep neural network\nmodels have only been utilized in limited ways.","url_abs":"http://arxiv.org/abs/1805.11204v2","url_pdf":"http://arxiv.org/pdf/1805.11204v2.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":"a-statistical-recurrent-model-on-the-manifold","repo_url":"https://github.com/zhenxingjian/SPD-SRU","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1805.11204","atlas_url":"https://app.syntology.ai/?focus=1805.11204","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}