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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.
Index Terms- Dimensionality reduction, principal curves, principal surfaces, density estimation, model selection, kernel methods.

S. Klanke, H. Ritter, P. Meinicke and R. Memisevic, "Principal Surfaces from Unsupervised Kernel Regression," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 27, no. , pp. 1379-1391, 2005.
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