Correlations between random projections and the bivariate normal

摘要

Random projections is a technique primarily used in dimension reduction by mapping high dimensional data to a low dimensional space, preserving pairwise distances in expectation, such as the Euclidean distance, inner product, angular distance, and \(l_p\) distance for values of p which are even. These estimated pairwise distances between observations in the low dimensional space can be rapidly computed to be used for nearest neighbor searches, clustering, or even classification. This paper highlights how these two disparate topics have a common thread, and expand upon two computational statistical techniques in recent random projection literature to further improve the accuracy of the estimate of the inner product between vectors under random projection by making use of the properties of the respective dataset, as well as limitations of these methods.