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Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

Einbeck, Jochen, Tutz, Gerhard & Evers, Ludger (2005), Exploring Multivariate Data Structures with Local Principal Curves, in Weihs, C. & Gaul, W. eds, Studies in classification data analysis and knowledge organization 28th Annual Conference of the German Classification Society. Magedeburg, Germany, Springer-Verlag, Magedeburg, 256-263.

Author(s) from Durham

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.