{"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/analyzing-linear-dynamical-systems-from","title":"Analyzing Linear Dynamical Systems: From Modeling to Coding and Learning","arxiv_id":"1608.01059","date":"2016-08-03","proceeding":null,"authors":["Wenbing Huang","Fuchun Sun","Lele Cao","Mehrtash Harandi"],"abstract":"Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich\nmodels with applications ranging from dynamical texture recognition to video\nsegmentation to name a few. In this paper, we propose to represent LDSs with\ninfinite-dimensional subspaces and derive an analytic solution to obtain stable\nLDSs. We then devise efficient algorithms to perform sparse coding and\ndictionary learning on the space of infinite-dimensional subspaces. In\nparticular, two solutions are developed to sparsely encode an LDS. In the first\nmethod, we map the subspaces into a Reproducing Kernel Hilbert Space (RKHS) and\nachieve our goal through kernel sparse coding. As for the second solution, we\npropose to embed the infinite-dimensional subspaces into the space of symmetric\nmatrices and formulate the sparse coding accordingly in the induced space. For\ndictionary learning, we encode time-series by introducing a novel concept,\nnamely the two-fold LDSs. We then make use of the two-fold LDSs to derive an\nanalytical form for updating atoms of an LDS dictionary, i.e., each atom is an\nLDS itself. Compared to several baselines and state-of-the-art methods, the\nproposed methods yield higher accuracies in various classification tasks\nincluding video classification and tactile recognition.","url_abs":"http://arxiv.org/abs/1608.01059v2","url_pdf":"http://arxiv.org/pdf/1608.01059v2.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":"analyzing-linear-dynamical-systems-from","repo_url":"https://github.com/caolele/caolele.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"video-classification","task_name":"Video Classification"},{"task_slug":"video-segmentation","task_name":"Video Segmentation"},{"task_slug":"video-semantic-segmentation","task_name":"Video Semantic Segmentation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}