{"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-dynamic-distribution-decomposition","title":"Sparse Dynamic Distribution Decomposition: Efficient Integration of Trajectory and Snapshot Time Series Data","arxiv_id":"2006.05138","date":"2020-06-09","proceeding":null,"authors":["Jake P. Taylor-King","Cristian Regep","Jyothish Soman","Flawnson Tong","Catalina Cangea","Charlie Roberts"],"abstract":"Dynamic Distribution Decomposition (DDD) was introduced in Taylor-King et. al. (PLOS Comp Biol, 2020) as a variation on Dynamic Mode Decomposition. In brief, by using basis functions over a continuous state space, DDD allows for the fitting of continuous-time Markov chains over these basis functions and as a result continuously maps between distributions. The number of parameters in DDD scales by the square of the number of basis functions; we reformulate the problem and restrict the method to compact basis functions which leads to the inference of sparse matrices only -- hence reducing the number of parameters. Finally, we demonstrate how DDD is suitable to integrate both trajectory time series (paired between subsequent time points) and snapshot time series (unpaired time points). Methods capable of integrating both scenarios are particularly relevant for the analysis of biomedical data, whereby studies observe population at fixed time points (snapshots) and individual patient journeys with repeated follow ups (trajectories).","url_abs":"https://arxiv.org/abs/2006.05138v2","url_pdf":"https://arxiv.org/pdf/2006.05138v2.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-dynamic-distribution-decomposition","repo_url":"https://github.com/RelationRx/SparseDDD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}