Persistent Cohomology and Circular Coordinates

@article{Silva2011PersistentCA,
  title={Persistent Cohomology and Circular Coordinates},
  author={Vin de Silva and Dmitriy Morozov and Mikael Vejdemo-Johansson},
  journal={Discrete \& Computational Geometry},
  year={2011},
  volume={45},
  pages={737-759}
}
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE, and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low-dimensional coordinates which represent the intrinsic structure of the data. This paradigm incorporates the assumption that real-valued coordinates provide a rich enough class of functions to represent the data faithfully and efficiently. On the other hand, there are simple structures which challenge this assumption… 
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