Kernel Sliced Inverse Regression: Regularization and Consistency

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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Bibliographic Details
Main Authors: Qiang Wu, Feng Liang, Sayan Mukherjee
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/540725
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spelling doaj-fcb1bdb61c4146f192bee09ea42bfd062020-11-25T02:27:12ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Qiang Wu
Feng Liang
Sayan Mukherjee
spellingShingle Qiang Wu
Feng Liang
Sayan Mukherjee
Kernel Sliced Inverse Regression: Regularization and Consistency
Abstract and Applied Analysis
author_facet Qiang Wu
Feng Liang
Sayan Mukherjee
author_sort Qiang Wu
title Kernel Sliced Inverse Regression: Regularization and Consistency
title_short 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_sort kernel sliced inverse regression: regularization and consistency
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/540725
work_keys_str_mv AT qiangwu kernelslicedinverseregressionregularizationandconsistency
AT fengliang kernelslicedinverseregressionregularizationandconsistency
AT sayanmukherjee kernelslicedinverseregressionregularizationandconsistency
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