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Figure . . he monkey neural pulses dataset, showing the separation achieved by the first two of the
nine (out of a total of ) parameters obtained from the dimensionality selection
he rules are explicit, “visualizable” and yield dimensionality selection choosing and
ordering the minimal set of variables needed to state the rule without loss of infor-
mation. here are variations that apply to some situations where the NC classifier
fails, such as the presence of several large “holes” (see Inselberg and Avidan ( )).
Further, the fact that the classification rule is the result of several iterations suggests
heuristics for dealing with the pesky problem of over-fitting. he iterations can be
stoppedwhenthecorrections inEq. . becomeverysmall,i.e., S i consists ofasmall
number of points. he number of iterations is user-defined, and the resulting rule
yieldsanerrorduringtheteststagethatismorestableundervariationsinthenumber
of points of the test set. In addition, the user can exclude variables from being used
in the description of the rule; those ordered last are the ones that provide the smaller
corrections and hence are more liable to over-correct.
Visual and Computational Models
14.4
Finally,weillustratethemethodology'sabilitytomodelmultivariaterelationsinterms
of hypersurfaces - just as we model a relation between two variables by a planar re-
gion. hen, by using the interior point algorithm, as shown for example in Fig. . ,
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