Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization
Abstract
We introduce a technique for dimensionality estimation based on the notion of quantization dimension, which connects the asymptotic optimal quantization error for a probability distribution on a manifold to its intrinsic dimension. The definition of quantization dimension yields a family of estimation algorithms, whose limiting case is equivalent to a recent method based on packing numbers. Using the formalism of high-rate vector quantization, we address issues of statistical consistency and analyze the behavior of our scheme in the presence of noise.
Cite
Text
Raginsky and Lazebnik. "Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization." Neural Information Processing Systems, 2005.Markdown
[Raginsky and Lazebnik. "Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization." Neural Information Processing Systems, 2005.](https://mlanthology.org/neurips/2005/raginsky2005neurips-estimation/)BibTeX
@inproceedings{raginsky2005neurips-estimation,
title = {{Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization}},
author = {Raginsky, Maxim and Lazebnik, Svetlana},
booktitle = {Neural Information Processing Systems},
year = {2005},
pages = {1105-1112},
url = {https://mlanthology.org/neurips/2005/raginsky2005neurips-estimation/}
}