Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization

We introduce a technique for dimensionality estimation based on the no- tion of quantization dimension, which connects the asymptotic optimal quantization error for a probability distribution on a mani fold to its intrin- sic dimension. The definition of quantization dimension yie lds 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 cons istency and ana- lyze the behavior of our scheme in the presence of noise.