Locally Defined Principal Curves and Surfaces

@article{Ozertem2011LocallyDP,
  title={Locally Defined Principal Curves and Surfaces},
  author={Umut Ozertem and Deniz Erdoğmuş},
  journal={J. Mach. Learn. Res.},
  year={2011},
  volume={12},
  pages={1249-1286}
}
Principal curves are defined as self-consistent smooth curves passing through the middle of the data, and they have been used in many applications of machine learning as a generalization, dimensionality reduction and a feature extraction tool. We redefine principal curves and surfaces in terms of the gradient and the Hessian of the probability density estimate. This provides a geometric understanding of the principal curves and surfaces, as well as a unifying view for clustering, principal… 

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