An axiomatic approach to intrinsic dimension of a dataset

@article{Pestov2008AnAA,
  title={An axiomatic approach to intrinsic dimension of a dataset},
  author={Vladimir Pestov},
  journal={Neural networks : the official journal of the International Neural Network Society},
  year={2008},
  volume={21 2-3},
  pages={204-13}
}
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper. The main features of our approach are that a high intrinsic dimension of a dataset reflects the presence of the curse of dimensionality (in a certain mathematically precise sense), and that dimension of a discrete i.i.d. sample of a low-dimensional manifold is, with high probability, close to that of the manifold. At the same time, the intrinsic… CONTINUE READING
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