{"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/geometric-insights-into-support-vector","title":"Geometric Insights into Support Vector Machine Behavior using the KKT Conditions","arxiv_id":"1704.00767","date":"2017-04-03","proceeding":null,"authors":["Iain Carmichael","J. S. Marron"],"abstract":"The support vector machine (SVM) is a powerful and widely used classification\nalgorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide\nrigorous mathematical proof for new insights into the behavior of SVM. These\ninsights provide perhaps unexpected relationships between SVM and two other\nlinear classifiers: the mean difference and the maximal data piling direction.\nFor example, we show that in many cases SVM can be viewed as a cropped version\nof these classifiers. By carefully exploring these connections we show how SVM\ntuning behavior is affected by characteristics including: balanced vs.\nunbalanced classes, low vs. high dimension, separable vs. non-separable data.\nThese results provide further insights into tuning SVM via cross-validation by\nexplaining observed pathological behavior and motivating improved\ncross-validation methodology. Finally, we also provide new results on the\ngeometry of complete data piling directions in high dimensional space.","url_abs":"http://arxiv.org/abs/1704.00767v2","url_pdf":"http://arxiv.org/pdf/1704.00767v2.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":"geometric-insights-into-support-vector","repo_url":"https://github.com/idc9/svm_geometry","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"svm","method_name":"SVM"}],"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}