Principal surfaces from unsupervised kernel regression

Meinicke P, Klanke S, Memisevic R, Ritter H (2005)
IEEE Transactions on Pattern Analysis and Machine Intelligence 27(9): 1379-1391.

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Abstract
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.
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Meinicke P, Klanke S, Memisevic R, Ritter H. Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2005;27(9):1379-1391.
Meinicke, P., Klanke, S., Memisevic, R., & Ritter, H. (2005). Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(9), 1379-1391.
Meinicke, P., Klanke, S., Memisevic, R., and Ritter, H. (2005). Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence 27, 1379-1391.
Meinicke, P., et al., 2005. Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(9), p 1379-1391.
P. Meinicke, et al., “Principal surfaces from unsupervised kernel regression”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, 2005, pp. 1379-1391.
Meinicke, P., Klanke, S., Memisevic, R., Ritter, H.: Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Machine Intelligence. 27, 1379-1391 (2005).
Meinicke, Peter, Klanke, Stefan, Memisevic, R., and Ritter, Helge. “Principal surfaces from unsupervised kernel regression”. IEEE Transactions on Pattern Analysis and Machine Intelligence 27.9 (2005): 1379-1391.
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