Model selection using support
vector machines (SVM) has been widely applied and investigated in the radial
basis functions (RBF) kernels case. The time consumption has been reduced
meaningfully using smooth upper bounds on the generalization ability. However,
there have been no conclusions about the analytical structure of the rule that
generates the data and labels it. In this work we present a simple model selection
algorithm for polynomial kernel SVM that results in tuning the polynomial
degree of the used kernel to the best fit value. We show that this procedure
provides us with some understanding of the analytical behavior of the
generating rule of the data, assuming it is polynomial. Although the procedure
is a heavy time consumer and many improvements from the RBF SVM model selection
cannot be applied to it, it can be very helpful in understanding ``nature
rules'' and analyzing certain qualities and behaviors. We present the case of
the 2D circle recognition among 2D geometrical shapes, and show that some
conclusions can be reached concerning the properties of circles that separate
them from other geometrical shapes. A training sample consists of feature
vectors of various properties of 2D shapes. A feature selection procedure can
be applied to this data, choosing a partial set of features. The remaining
features will be the discriminating ones; the area and the perimeter of the
shape. The system is trained with various oracles that are a result of
different mistake factors. One of the oracles is an average vote of a number of
people. We show that the resulting system's success rate is better than the
best member of the oracle group, and that the model selection procedure yields
a quadratic relation between the area and the perimeter of the shape, a known
mathematical fact.
