## Fractal-Based Intrinsic Dimension Estimation and Its Application in Dimensionality Reduction

- Dengyao Mo, Samuel H. Huang
- IEEE Transactions on Knowledge and Data…
- 2012

@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} }

- Published 2008 in Neural Networks
DOI:10.1016/j.neunet.2007.12.030

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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