Nonlinear Dimension Reduction with Kernel Sliced Inverse Regression

2009 ◽  
Vol 21 (11) ◽  
pp. 1590-1603 ◽  
Author(s):  
Yi-Ren Yeh ◽  
Su-Yun Huang ◽  
Yuh-Jye Lee
Keyword(s):  
Dimension Reduction ◽  
Sliced Inverse Regression ◽  
Inverse Regression ◽  
Nonlinear Dimension Reduction ◽  
Nonlinear Dimension

scholarly journals Kernel Sliced Inverse Regression: Regularization and Consistency

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qiang Wu ◽  
Feng Liang ◽  
Sayan Mukherjee
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Sliced Inverse Regression ◽  
Inverse Regression ◽  
Computational Stability ◽  
Generalization Performance ◽  
Nonlinear Dimension Reduction ◽  
Nonlinear Dimension

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.

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