Principal Surfaces from Unsupervised Kernel Regression
IEEE Transactions on Pattern Analysis and Machine Intelligence
A web server for automatic analysis and extraction of relevant biological knowledge
Computers in Biology and Medicine
Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS
Neural Information Processing
IEEE Transactions on Signal Processing
Principal curves with feature continuity
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Similarity preserving principal curve: an optimal 1-D feature extractor for data representation
IEEE Transactions on Neural Networks
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
Clustering based on principal curve
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
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Principal curves, like principal components, are a tool used in multivariate analysis for ends like feature extraction. Defined in their original form, principal curves need not exist for general distributions. The existence of principal curves with bounded length for any distribution that satisfies some minimal regularity conditions has been shown. We define principal curves with bounded turn, show that they exist, and present a learning algorithm for them. Principal components are a special case of such curves when the turn is zero.