Self-organizing maps
GTM: the generative topographic mapping
Neural Computation
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Regularized principal manifolds
The Journal of Machine Learning Research
Principal Surfaces from Unsupervised Kernel Regression
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
A leave-k-out cross-validation scheme for unsupervised kernel regression
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Fundamenta Informaticae - Intelligent Data Analysis in Granular Computing
Evolutionary kernel density regression
Expert Systems with Applications: An International Journal
On evolutionary approaches to unsupervised nearest neighbor regression
EvoApplications'12 Proceedings of the 2012t European conference on Applications of Evolutionary Computation
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We present an extension to unsupervised kernel regression (UKR), a recent method for learning of nonlinear manifolds, which can utilize leave-one-out cross-validation as an automatic complexity control without additional computational cost. Our extension allows us to incorporate general cost functions, by which the UKR algorithm can be made more robust or be tuned to specific noise models. We focus on Huber's loss and on the @e-insensitive loss, which we present together with a practical optimization approach. We demonstrate our method on both toy and real data.