Approximate distance clustering

We address the problem of statistical pattern recognition (clustering, classification, discriminant analysis) for n observations in d-dimensionaI Euclidean space when n much less than d. As such, we are concerned with circumventing the "curse of dimensionality." Our approach, termed "approximate distance clustering," is motivated by dimensionality reduction methods which embed points from a high-dimensional Euclidean space into a lower dimensional space while approximately preserving pairwise distances between points. The methodology involves non-linear projections based on inter-point distances to random subsets. Combinatorial algorithms are developed and theoretical, simulation, and experimental results are presented indicating that approximate distance clustering has application in many challenging pattern recognition scenarios.