New TR

[Roman Rosipal]

Dear Connectionists,

The following TR is now available at my home page:

Kernel Partial Least Squares Regression in RKHS

Roman  Rosipal and  Leonard J Trejo


 Abstract

A family of regularized least squares regression models in a
Reproducing Kernel Hilbert Space is extended by the Kernel Partial
Least Squares (PLS) regression model.  Similar to Principal Components
Regression (PCR), PLS is a method based on the projection of input
(explanatory) variables to the latent variables (components). However,
in contrast to PCR, PLS creates the components by modeling the
relationship between input andoutput variables while maintaining most
of the input variables information. PLS is considered to be useful in
situations where the number of explanatory variables exceeds the
number of observations and/or a high level of multicollinearityamong
those variables is assumed. Motivated by this fact we will provide a
Kernel PLS algorithm for construction of non-linear regression models
in possiblyhigh-dimensional feature spaces.
  
We give the theoretical description of the Kernel PLS algorithm and we
experimentally compare the algorithm with the existing Kernel PCR and
Kernel Ridge Regression techniques.  We will demonstrate that on the
data sets employed Kernel PLS achieves the same results but in
comparison to Kernel PCR uses significantly smaller, qualitatively
different components.
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You can download gzipped postscript from

 http://cis.paisley.ac.uk/rosi-ci0/Papers/TR01_1.ps.gz

 Any comments and remarks are very  welcome.

 _______________


 Roman Rosipal
 University of Paisley,
 CIS Department,
 Paisley, PA1 2BE
 Scotland, UK
 http://cis.paisley.ac.uk/rosi-ci0
 e-mai:rosi-ci0 at paisley.ac.uk



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