<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bartkowiak, A.</style></author><author><style face="normal" font="default" size="100%">Evelpidou, N.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Visualization of multivariate data with additional class information.</style></title><secondary-title><style face="normal" font="default" size="100%">ACS -CISIM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The goal is to visualize a set of multivariate data in such a way that data&lt;br&gt;vectors belonging to different classes (subgroups) appear differentiated as much&lt;br&gt;as possible. When intending such visualization, the first question should be about&lt;br&gt;the intrinsic dimensionality of the data. The answer may be obtained by&lt;br&gt;evaluating, e.g., the fractal correlation dimension. The projection to a plane is&lt;br&gt;justified when the correlation dimension of the data is about 2. Only in such case&lt;br&gt;the performed visualization is plausible to reflect all the between group and the&lt;br&gt;within group relationships among the data vectors. There are several recognized&lt;br&gt;methods for mapping data to a plane. Our interest lies especially in nonlinear&lt;br&gt;methods. We consider in detail three methods: The canonical discriminant&lt;br&gt;functions, the kernel discriminant functions and the neuroscale mapping. We&lt;br&gt;illustrate our considerations using the Kefallinia erosion data, where each data&lt;br&gt;vector belongs - in a crisp way – to one of five predefined subgroups indicating&lt;br&gt;the severity of the erosion risk. The assignments to the subgroups were performed&lt;br&gt;by an expert GIS system based on logical rules established by experts.&lt;/p&gt;</style></abstract></record></records></xml>