Spherical random projection

Abstract

We propose a new method for dimension reduction of high-dimensional spherical data based on the nonlinear projection of sphere-valued data to a randomly chosen subsphere. The proposed method, spherical random projection, leads to a probabilistic lower-dimensional mapping of spherical data into a subsphere of the original. In this paper, we investigate some properties of spherical random projection, including expectation preservation and distance concentration, from which we derive an analogue of the Johnson–Lindenstrauss Lemma for spherical random projection. Clustering model selection is discussed as an application of spherical random projection, and numerical experiments are conducted using real and simulated data.