Classification using geometric level sets
A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learn...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery (ACM)
2012
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| Online Access: | http://hdl.handle.net/1721.1/72004 https://orcid.org/0000-0003-0149-5888 |
| _version_ | 1811093011501678592 |
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| author | Varshney, Kush R. Willsky, Alan S. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Varshney, Kush R. Willsky, Alan S. |
| author_sort | Varshney, Kush R. |
| collection | MIT |
| description | A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learning: the surface area of the decision boundary. This geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its ε-entropy. For multicategory classification, an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions. Geometric level set classification yields performance results on benchmark data sets that are competitive with well-established methods. |
| first_indexed | 2024-09-23T15:38:09Z |
| format | Article |
| id | mit-1721.1/72004 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:38:09Z |
| publishDate | 2012 |
| publisher | Association for Computing Machinery (ACM) |
| record_format | dspace |
| spelling | mit-1721.1/720042022-09-29T15:09:30Z Classification using geometric level sets Varshney, Kush R. Willsky, Alan S. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Willsky, Alan S. Varshney, Kush R. Willsky, Alan S. A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learning: the surface area of the decision boundary. This geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its ε-entropy. For multicategory classification, an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions. Geometric level set classification yields performance results on benchmark data sets that are competitive with well-established methods. National Science Foundation (U.S.) (Graduate Research Fellowship) United States. Army Research Office (MURI grant W911NF-06-1-0076) 2012-08-07T13:08:32Z 2012-08-07T13:08:32Z 2010-02 2009-08 Article http://purl.org/eprint/type/JournalArticle 1532-4435 1533-7928 http://hdl.handle.net/1721.1/72004 Kush R. Varshney and Alan S. Willsky. 2010. Classification Using Geometric Level Sets. J. Mach. Learn. Res. 11 (March 2010), 491-516. https://orcid.org/0000-0003-0149-5888 en_US http://dl.acm.org/citation.cfm?id=1756020 Journal of Machine Learning Research Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Association for Computing Machinery (ACM) Willsky via Amy Stout |
| spellingShingle | Varshney, Kush R. Willsky, Alan S. Classification using geometric level sets |
| title | Classification using geometric level sets |
| title_full | Classification using geometric level sets |
| title_fullStr | Classification using geometric level sets |
| title_full_unstemmed | Classification using geometric level sets |
| title_short | Classification using geometric level sets |
| title_sort | classification using geometric level sets |
| url | http://hdl.handle.net/1721.1/72004 https://orcid.org/0000-0003-0149-5888 |
| work_keys_str_mv | AT varshneykushr classificationusinggeometriclevelsets AT willskyalans classificationusinggeometriclevelsets |