Nonlinear principal component analysis.

Authors: 
Der, Ralf
Steinmetz, Ulrich
Balzuweit, Gerd
Schüürmann, Gerrit
Year: 
1998
Language: 
English
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.
Appeared / Erschienen in: 
Report Nr. 4/1998 des Instituts fuer Informatik der Universitaet Leipzig
Pubdate / Erscheinungsdatum: 
1998
Pages / Seitenanzahl: 
19
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