{"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/introducing-user-prescribed-constraints-in","title":"Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction","arxiv_id":"1806.05096","date":"2018-06-13","proceeding":null,"authors":["Purushottam D. Dixit"],"abstract":"Stochastic kernel based dimensionality reduction approaches have become\npopular in the last decade. The central component of many of these methods is a\nsymmetric kernel that quantifies the vicinity between pairs of data points and\na kernel-induced Markov chain on the data. Typically, the Markov chain is fully\nspecified by the kernel through row normalization. However, in many cases, it\nis desirable to impose user-specified stationary-state and dynamical\nconstraints on the Markov chain. Unfortunately, no systematic framework exists\nto impose such user-defined constraints. Here, we introduce a path entropy\nmaximization based approach to derive the transition probabilities of Markov\nchains using a kernel and additional user-specified constraints. We illustrate\nthe usefulness of these Markov chains with examples.","url_abs":"http://arxiv.org/abs/1806.05096v2","url_pdf":"http://arxiv.org/pdf/1806.05096v2.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":"introducing-user-prescribed-constraints-in","repo_url":"https://github.com/dixitpd/maxcaldiffmap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}