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Abstract and Applied Analysis
Volume 2013, Article ID 540725, 11 pages
Research Article

Kernel Sliced Inverse Regression: Regularization and Consistency

1Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37130, USA
2Department of Statistics, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA
3Departments of Statistical Science, Mathematics, and Computer Science, Institute for Genome Sciences & Policy, Duke University, Durham, NC 27708, USA

Received 3 May 2013; Accepted 14 June 2013

Academic Editor: Yiming Ying

Copyright © 2013 Qiang Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.