{"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/mapper-comparison-with-wasserstein-metrics","title":"Mapper Comparison with Wasserstein Metrics","arxiv_id":"1812.06232","date":"2018-12-15","proceeding":null,"authors":["Michael McCabe"],"abstract":"The challenge of describing model drift is an open question in unsupervised\nlearning. It can be difficult to evaluate at what point an unsupervised model\nhas deviated beyond what would be expected from a different sample from the\nsame population. This is particularly true for models without a probabilistic\ninterpretation. One such family of techniques, Topological Data Analysis, and\nthe Mapper algorithm in particular, has found use in a variety of fields, but\ndescribing model drift for Mapper graphs is an understudied area as even\nexisting techniques for measuring distances between related constructs like\ngraphs or simplicial complexes fail to account for the fact that Mapper graphs\nrepresent a combination of topological, metric, and density information. In\nthis paper, we develop an optimal transport based metric which we call the\nNetwork Augmented Wasserstein Distance for evaluating distances between Mapper\ngraphs and demonstrate the value of the metric for model drift analysis by\nusing the metric to transform the model drift problem into an anomaly detection\nproblem over dynamic graphs.","url_abs":"http://arxiv.org/abs/1812.06232v1","url_pdf":"http://arxiv.org/pdf/1812.06232v1.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":"mapper-comparison-with-wasserstein-metrics","repo_url":"https://github.com/mikemccabe210/mapper_comparison","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"anomaly-detection","task_name":"Anomaly Detection"},{"task_slug":"open-question","task_name":"Open-Ended Question Answering"},{"task_slug":"topological-data-analysis","task_name":"Topological Data 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}