Exploring multivariate data structures with local principal curves

Abstract

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth "local principal curve" passing through the "middle" of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy. © Springer-Verlag Berlin, Heidelberg 2005.