Local principal curves

• DOI: 10.1007/s11222-005-4073-8
• Publication Date: 2005-10-11T16:14:51Z
• Authors: Jochen Einbeck; Gerhard Tutz; Ludger Evers
• Keywords: Mean shift; Principal components; Local smoothing; ddc:519; local smoothing; 01 natural sciences; Principal curves; 510; mean shift; principal curves; component analysis; 0101 mathematics; QA; principal components

Principal components are a well established tool in dimension reduction. The extension to principal curves allows for general smooth curves which pass through the middle of a p-dimensional data cloud. In this paper local principal curves are introduced, which are based on the localization of principal component analysis. The proposed algorithm is able to identify closed curves as well as multiple curves which may or may not be connected. For the evaluation of performance of data reduction obtained by principal curves a measure of coverage is suggested. The selection of tuning parameters is considered explicitely yielding an algorithm which is easy to apply. By use of simulated and real data sets the approach is compared to various alternative concepts of principal curves.