A concentration theorem for projections
Sanjoy Dasgupta, Daniel Hsu, Nakul Verma
X in R^D has mean zero and finite second moments. We show that there is a precise sense in which almost all linear projections of X into R^d (for d < D) look like a scale-mixture of spherical Gaussians -- specifically, a mixture of distributions N(0, sigma^2 I_d) where the weight of the particular sigma component is P (| X |^2 = sigma^2 D). The extent of this effect depends upon the ratio of d to D, and upon a particular coefficient of eccentricity of X's distribution. We explore this result in a variety of experiments.
PDF Link: /papers/06/p114-dasgupta.pdf
AUTHOR = "Sanjoy Dasgupta
and Daniel Hsu and Nakul Verma",
TITLE = "A concentration theorem for projections",
BOOKTITLE = "Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "114--121"