Publication Details |
Category | Text Publication |
Reference Category | Reports |
URL | https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-345209 |
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 | https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=23993 |
Der, R., Steinmetz, U., Balzuweit, G., Schüürmann, G. (1998): Nonlinear principal component analysis Report / Institut für Informatik 4/98 Universität Leipzig, Leipzig, 19 pp. |