[WIP] Proposed C parameter clarifications in RBF SVM parameter example (scikit-learn#8957)

* Proposed rewrite

* Update plot_rbf_parameters.py

use phrasing suggested by @vene.

Author: chrisfosterelli

examples/svm/plot_rbf_parameters.py

@@ -11,10 +11,12 @@
 'close'. The ``gamma`` parameters can be seen as the inverse of the radius of
 influence of samples selected by the model as support vectors.
 
-The ``C`` parameter trades off misclassification of training examples against
-simplicity of the decision surface. A low ``C`` makes the decision surface
-smooth, while a high ``C`` aims at classifying all training examples correctly
-by giving the model freedom to select more samples as support vectors.
+The ``C`` parameter trades off correct classification of training examples 
+against maximization of the decision function's margin. For larger values of 
+``C``, a smaller margin will be accepted if the decision function is better at 
+classifying all training points correctly. A lower ``C`` will encourage a larger 
+margin, therefore a simpler decision function, at the cost of training accuracy.
+In other words``C`` behaves as a regularization parameter in the SVM.
 
 The first plot is a visualization of the decision function for a variety of
 parameter values on a simplified classification problem involving only 2 input
@@ -46,16 +48,16 @@
 
 For intermediate values, we can see on the second plot that good models can
 be found on a diagonal of ``C`` and ``gamma``. Smooth models (lower ``gamma``
-values) can be made more complex by selecting a larger number of support
-vectors (larger ``C`` values) hence the diagonal of good performing models.
+values) can be made more complex by increasing the importance of classifying
+each point correctly (larger ``C`` values) hence the diagonal of good performing
+models.
 
 Finally one can also observe that for some intermediate values of ``gamma`` we
-get equally performing models when ``C`` becomes very large: it is not
-necessary to regularize by limiting the number of support vectors. The radius of
-the RBF kernel alone acts as a good structural regularizer. In practice though
-it might still be interesting to limit the number of support vectors with a
-lower value of ``C`` so as to favor models that use less memory and that are
-faster to predict.
+get equally performing models when ``C`` becomes very large: it is not necessary
+to regularize by enforcing a larger margin. The radius of the RBF kernel alone 
+acts as a good structural regularizer. In practice though it might still be 
+interesting to simplify the decision function with a lower value of ``C`` so as
+to favor models that use less memory and that are faster to predict.
 
 We should also note that small differences in scores results from the random
 splits of the cross-validation procedure. Those spurious variations can be