Estimation of Intrinsic Dimensionality Using High-Rate Vector Quantization

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

Bibtex Metadata Paper


Maxim Raginsky, Svetlana Lazebnik


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.