Randomized Nonlinear Projections Uncover High-Dimensional Structure
Lenore Cowen, Carey E. Priebe · Advances in Applied Mathematics · 1997
We consider the problem of investigating the “structure” of a set of points in high-dimensional space (npoints ind-dimensional Euclidean space) whenn ⪡ d. The analysis of such data sets is a notoriously difficult problem in both combinatorial optimization and statistics due to an exponential explosion ind. A randomized nonlinear projection method is presented that maps these observations to a low-dimensional space, while approximately preserving salient features of the original data. Classical statistical analyses can then be applied, and results from the multiple lower-dimensional projected spaces are combined to yield information about the high-dimensional structure. We apply our dimension reduction techniques to a pattern recognition problem involving PET scan brain volumes.