Kernel Sliced Inverse Regression: Regularization and Consistency
Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/540725 |
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| _version_ | 1832553372471787520 |
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| author | Qiang Wu Feng Liang Sayan Mukherjee |
| author_facet | Qiang Wu Feng Liang Sayan Mukherjee |
| author_sort | Qiang Wu |
| collection | DOAJ |
| description | Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data. |
| format | Article |
| id | doaj-art-fcb1bdb61c4146f192bee09ea42bfd06 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fcb1bdb61c4146f192bee09ea42bfd062025-02-03T05:54:15ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/540725540725Kernel Sliced Inverse Regression: Regularization and ConsistencyQiang Wu0Feng Liang1Sayan Mukherjee2Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37130, USADepartment of Statistics, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USADepartments of Statistical Science, Mathematics, and Computer Science, Institute for Genome Sciences & Policy, Duke University, Durham, NC 27708, USAKernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data.http://dx.doi.org/10.1155/2013/540725 |
| spellingShingle | Qiang Wu Feng Liang Sayan Mukherjee Kernel Sliced Inverse Regression: Regularization and Consistency Abstract and Applied Analysis |
| title | Kernel Sliced Inverse Regression: Regularization and Consistency |
| title_full | Kernel Sliced Inverse Regression: Regularization and Consistency |
| title_fullStr | Kernel Sliced Inverse Regression: Regularization and Consistency |
| title_full_unstemmed | Kernel Sliced Inverse Regression: Regularization and Consistency |
| title_short | Kernel Sliced Inverse Regression: Regularization and Consistency |
| title_sort | kernel sliced inverse regression regularization and consistency |
| url | http://dx.doi.org/10.1155/2013/540725 |
| work_keys_str_mv | AT qiangwu kernelslicedinverseregressionregularizationandconsistency AT fengliang kernelslicedinverseregressionregularizationandconsistency AT sayanmukherjee kernelslicedinverseregressionregularizationandconsistency |