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in groups F 15 and F 20 . However, Gaussian kernel produces stable and accurate
results for all test datasets, including sets of elements in free groups of large
ranks. This indicates that points in one of the classes (minimal or non-minimal)
are compactly distributed in the feature space and can be accurately described
as a Gaussian. We also can observe that Gaussian representation can be applied
to only one of the classes. If the opposite was true, then the problem of separat-
ing the two classes would be much simpler and at least the quadratic mapping
should have been as accurate as K e .
We conclude this section with the following conclusions:
1. With appropriate kernel function Support Vector Machines approach per-
forms very well in the task of classification of Whitehead-minimal words in
free groups of various ranks, including groups of large ranks.
2. The best over all results are obtained with the Gaussian kernel K e . This in-
dicates that one of the classes is compact and can be bounded by a Gaussian
function.
3. Regression approach is still would be preferable for groups of small ranks
due to its simplicity and smaller resource requirements. However, the SMVs
should be used for groups of larger ranks where the size of the training
sets required to perform regression with non-linear preprocessing mapping
becomes practically intractable.
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