Publication Details

Category Text Publication
Reference Category Reports
Title (Primary) Nonlinear principal component analysis
Author Der, R.; Steinmetz, U.; Balzuweit, G.; Schüürmann, G.
Journal Report / Institut für Informatik
Year 1998
Department OEC; COE
Volume 4/98
Page To 19
Language englisch
Abstract We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster structures in a set of real world data from the domain of ecotoxicology.
Persistent UFZ Identifier
Der, R., Steinmetz, U., Balzuweit, G., Schüürmann, G. (1998):
Nonlinear principal component analysis
Report / Institut für Informatik 4/98
Universität Leipzig, Leipzig, 19 pp.