Estimation of intrinsic dimensionality using high-rate vector quantization

Опубликовано 6 сентября 2016, 6:05

Joint work with Svetlana Lazebnik at UIUC. In this talk, I will describe 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, I will discuss issues of statistical consistency and sensitivity to noise, and present results on real and simulated data.