Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization

We introduce a technique for dimensionality estimation based on the notion ofquantization 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 thebehavior of our scheme in the presence of noise.