Principal surfaces from unsupervised kernel regression.
We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the Nadaraya-Watson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides a practical solution to the model selection problem because all parameters can be estimated by leave-one-out cross-validation without additional computational cost. In addition, our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization, beyond classical initializations based on linear PCA. Furthermore, it shows a simple way to fit principal surfaces in general feature spaces, beyond the usual data space setup. The experimental results illustrate these convenient features on simulated and real data.
Meinicke
Peter
P
P. Meinicke is with the Bioinformatics Department, Faculty of Biology, University of Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany. pmeinic@gwdg.de
Klanke
Stefan
S
Memisevic
Roland
R
Ritter
Helge
H
D000465:Algorithms; D001185:Artificial Intelligence; D016247:Information Storage and Retrieval / Q000379:methods; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*; D025341:Principal Component Analysis