{"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/sparse-coding-and-dictionary-learning-for","title":"Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach","arxiv_id":"1304.4344","date":"2013-04-16","proceeding":null,"authors":["Mehrtash T. Harandi","Conrad Sanderson","Richard Hartley","Brian C. Lovell"],"abstract":"Recent advances suggest that a wide range of computer vision problems can be\naddressed more appropriately by considering non-Euclidean geometry. This paper\ntackles the problem of sparse coding and dictionary learning in the space of\nsymmetric positive definite matrices, which form a Riemannian manifold. With\nthe aid of the recently introduced Stein kernel (related to a symmetric version\nof Bregman matrix divergence), we propose to perform sparse coding by embedding\nRiemannian manifolds into reproducing kernel Hilbert spaces. This leads to a\nconvex and kernel version of the Lasso problem, which can be solved\nefficiently. We furthermore propose an algorithm for learning a Riemannian\ndictionary (used for sparse coding), closely tied to the Stein kernel.\nExperiments on several classification tasks (face recognition, texture\nclassification, person re-identification) show that the proposed sparse coding\napproach achieves notable improvements in discrimination accuracy, in\ncomparison to state-of-the-art methods such as tensor sparse coding, Riemannian\nlocality preserving projection, and symmetry-driven accumulation of local\nfeatures.","url_abs":"http://arxiv.org/abs/1304.4344v1","url_pdf":"http://arxiv.org/pdf/1304.4344v1.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":"sparse-coding-and-dictionary-learning-for","repo_url":"https://github.com/chengcv/J3S","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"face-recognition","task_name":"Face Recognition"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"person-re-identification","task_name":"Person Re-Identification"},{"task_slug":"texture-classification","task_name":"Texture Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}