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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:34520 |
| Date | 15 July 2019 |
| Creators | Der, Ralf, Steinmetz, Ulrich, Balzuweit, Gerd, Schüürmann, Gerrit |
| Publisher | Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:book, info:eu-repo/semantics/book, doc-type:Text |
| Source | Report / Institut für Informatik, Report / Institut für Informatik |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | urn:nbn:de:bsz:15-qucosa2-343029, qucosa:34302 |
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