[MRG+1] DOC adding a warning on the relation between C and alpha (#7860)

dalmia · TomDLT · commit 8793ec96b233 · 2016-11-29T20:13:28.000+01:00
* DOC adding a warning on the relation between C and alpha

* DOC removing extra character

* DOC: changes to the relation described

* DOC fixing typo

* DOC fixing typo

* DOC fixing link to Ridge

* DOC link enhancement

* DOC fixing line length
diff --git a/doc/modules/linear_model.rst b/doc/modules/linear_model.rst
@@ -266,6 +266,13 @@ They also tend to break when the problem is badly conditioned
 
   * :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_model_selection.py`
 
+Comparison with the regularization parameter of SVM
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The equivalence between ``alpha`` and the regularization parameter of SVM,
+``C`` is given by ``alpha = 1 / C`` or ``alpha = 1 / (n_samples * C)``, 
+depending on the estimator and the exact objective function optimized by the
+model.
 
 .. _multi_task_lasso:
 
diff --git a/doc/modules/svm.rst b/doc/modules/svm.rst
@@ -600,8 +600,11 @@ The decision function is:
 .. note::
 
     While SVM models derived from `libsvm`_ and `liblinear`_ use ``C`` as
-    regularization parameter, most other estimators use ``alpha``. The relation
-    between both is :math:`C = \frac{n\_samples}{alpha}`.
+    regularization parameter, most other estimators use ``alpha``. The exact
+    equivalence between the amount of regularization of two models depends on
+    the exact objective function optimized by the model. For example, when the
+    estimator used is :class:`sklearn.linear_model.Ridge <ridge>` regression,
+    the relation between them is given as :math:`C = \frac{1}{alpha}`.
 
 .. TODO multiclass case ?/
 
