Regularization-free principal curve estimation

@article{Gerber2013RegularizationfreePC,
  title={Regularization-free principal curve estimation},
  author={Samuel Gerber and Ross T. Whitaker},
  journal={J. Mach. Learn. Res.},
  year={2013},
  volume={14},
  pages={1285-1302}
}
Principal curves and manifolds provide a framework to formulate manifold learning within a statistical context. Principal curves define the notion of a curve passing through the middle of a distribution. While the intuition is clear, the formal definition leads to some technical and practical difficulties. In particular, principal curves are saddle points of the mean-squared projection distance, which poses severe challenges for estimation and model selection. This paper demonstrates that the… 

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