TR available

[Roman Rosipal]

Dear Connectionists,

 The following TR is now available at my home page: 

 Kernel Principal Component Regression with EM Approach to Nonlinear Principal 
 Components Extraction

 R. Rosipal, LJ Trejo, A. Cichocki

 Abstract

 In kernel based methods such as Support Vector Machines, Kernel PCA,
Gaussian Processes or Regularization Networks the computational
requirements scale as O(n^3) where n is the number of training
points. In this paper we investigate Kernel Principal Component
Regression (KPCR) with the Expectation Maximization approach in
estimating of the subset of p principal components (p < n) in a
feature space defined by a positive definite kernel function. The
computational requirements of the method are O(pn^2). Moreover, the
algorithm can be implemented with memory requirements
O(p^2)+O((p+1)n)). We give the theoretical description explaining how
by the proper selection of a subset of non-linear principal components
desired generalization of the KPCR is achieved. On two data sets we
experimentally demonstrate this fact. Moreover, on a noisy chaotic
Mackey-Glass time series prediction the best performance is achieved
with p << n and experiments also suggests that in such cases we can
also use significantly reduced training data sets to estimate the
non-linear principal components. The theoretical relation and
experimental comparison to Kernel Ridge Regression and
epsilon-insensitive Support Vector Regression is also given.
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 You can download gzipped postscript from 

 http://cis.paisley.ac.uk/rosi-ci0/Papers/TR00_2.ps.gz 


 Any comments and remarks are 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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