{"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/visualizing-the-effects-of-a-changing","title":"Visualizing the Effects of a Changing Distance on Data Using Continuous Embeddings","arxiv_id":"1311.1911","date":"2013-11-08","proceeding":null,"authors":["Gina Gruenhage","Manfred Opper","Simon Barthelme"],"abstract":"Most Machine Learning (ML) methods, from clustering to classification, rely\non a distance function to describe relationships between datapoints. For\ncomplex datasets it is hard to avoid making some arbitrary choices when\ndefining a distance function. To compare images, one must choose a spatial\nscale, for signals, a temporal scale. The right scale is hard to pin down and\nit is preferable when results do not depend too tightly on the exact value one\npicked. Topological data analysis seeks to address this issue by focusing on\nthe notion of neighbourhood instead of distance. It is shown that in some cases\na simpler solution is available. It can be checked how strongly distance\nrelationships depend on a hyperparameter using dimensionality reduction. A\nvariant of dynamical multi-dimensional scaling (MDS) is formulated, which\nembeds datapoints as curves. The resulting algorithm is based on the\nConcave-Convex Procedure (CCCP) and provides a simple and efficient way of\nvisualizing changes and invariances in distance patterns as a hyperparameter is\nvaried. A variant to analyze the dependence on multiple hyperparameters is also\npresented. A cMDS algorithm that is straightforward to implement, use and\nextend is provided. To illustrate the possibilities of cMDS, cMDS is applied to\nseveral real-world data sets.","url_abs":"http://arxiv.org/abs/1311.1911v3","url_pdf":"http://arxiv.org/pdf/1311.1911v3.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":"visualizing-the-effects-of-a-changing","repo_url":"https://github.com/ginagruenhage/cmdsr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"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}