Self-organizing maps
GTM: the generative topographic mapping
Neural Computation
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Computation and Self-Organizing Maps; An Introduction
Neural Computation and Self-Organizing Maps; An Introduction
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Regularized principal manifolds
The Journal of Machine Learning Research
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA
Neural Computation
Principal curves with bounded turn
IEEE Transactions on Information Theory
2005 Special Issue: Improving dimensionality reduction with spectral gradient descent
Neural Networks - 2005 Special issue: IJCNN 2005
ICML '06 Proceedings of the 23rd international conference on Machine learning
Towards Semi-supervised Manifold Learning: UKR with Structural Hints
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Using structured UKR manifolds for motion classification and segmentation
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
A two-step framework for highly nonlinear data unfolding
Neurocomputing
Fundamenta Informaticae - Intelligent Data Analysis in Granular Computing
A manifold representation as common basis for action production and recognition
KI'09 Proceedings of the 32nd annual German conference on Advances in artificial intelligence
Similarity preserving principal curve: an optimal 1-D feature extractor for data representation
IEEE Transactions on Neural Networks
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
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
A particle swarm embedding algorithm for nonlinear dimensionality reduction
ANTS'12 Proceedings of the 8th international conference on Swarm Intelligence
Unsupervised nearest neighbors with kernels
KI'12 Proceedings of the 35th Annual German conference on Advances in Artificial Intelligence
Learning morphological maps of galaxies with unsupervised regression
Expert Systems with Applications: An International Journal
Regularization-free principal curve estimation
The Journal of Machine Learning Research
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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.