Abstract:

The goal is to visualize a set of multivariate data in such a way that data
vectors belonging to different classes (subgroups) appear differentiated as much
as possible. When intending such visualization, the first question should be about
the intrinsic dimensionality of the data. The answer may be obtained by
evaluating, e.g., the fractal correlation dimension. The projection to a plane is
justified when the correlation dimension of the data is about 2. Only in such case
the performed visualization is plausible to reflect all the between group and the
within group relationships among the data vectors. There are several recognized
methods for mapping data to a plane. Our interest lies especially in nonlinear
methods. We consider in detail three methods: The canonical discriminant
functions, the kernel discriminant functions and the neuroscale mapping. We
illustrate our considerations using the Kefallinia erosion data, where each data
vector belongs - in a crisp way – to one of five predefined subgroups indicating
the severity of the erosion risk. The assignments to the subgroups were performed
by an expert GIS system based on logical rules established by experts.