{"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/an-expectation-maximization-algorithm-for-the","title":"An Expectation-Maximization Algorithm for the Fractal Inverse Problem","arxiv_id":"1706.03149","date":"2017-06-09","proceeding":null,"authors":["Peter Bloem","Steven de Rooij"],"abstract":"We present an Expectation-Maximization algorithm for the fractal inverse\nproblem: the problem of fitting a fractal model to data. In our setting the\nfractals are Iterated Function Systems (IFS), with similitudes as the family of\ntransformations. The data is a point cloud in ${\\mathbb R}^H$ with arbitrary\ndimension $H$. Each IFS defines a probability distribution on ${\\mathbb R}^H$,\nso that the fractal inverse problem can be cast as a problem of parameter\nestimation. We show that the algorithm reconstructs well-known fractals from\ndata, with the model converging to high precision parameters. We also show the\nutility of the model as an approximation for datasources outside the IFS model\nclass.","url_abs":"http://arxiv.org/abs/1706.03149v2","url_pdf":"http://arxiv.org/pdf/1706.03149v2.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":"an-expectation-maximization-algorithm-for-the","repo_url":"https://github.com/pbloem/ifsem","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"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}