DOC fix the shape of `dual_coef_` in user guide documentation
@@ -175,9 +175,11 @@ The shape of ``dual_coef_`` is ``(n_classes-1, n_SV)`` with
a somewhat hard to grasp layout.
The columns correspond to the support vectors involved in any
of the ``n_classes * (n_classes - 1) / 2`` "one-vs-one" classifiers.
-Each of the support vectors is used in ``n_classes - 1`` classifiers.
-The ``n_classes - 1`` entries in each row correspond to the dual coefficients
-for these classifiers.
+Each support vector ``v`` has a dual coefficient in each of the
+``n_classes - 1`` classifiers comparing the class of ``v`` against another class.
+Note that some, but not all, of these dual coefficients, may be zero.
+The ``n_classes - 1`` entries in each column are these dual coefficients,
+ordered by the opposing class.
This might be clearer with an example: consider a three class problem with
class 0 having three support vectors
@@ -188,21 +190,14 @@ the coefficient of support vector :math:`v^{j}_i` in the classifier between
classes :math:`i` and :math:`k` :math:`\alpha^{j}_{i,k}`.
Then ``dual_coef_`` looks like this:
-+------------------------+------------------------+------------------+
-|:math:`\alpha^{0}_{0,1}`|:math:`\alpha^{0}_{0,2}`|Coefficients |
-+------------------------+------------------------+for SVs of class 0|
-|:math:`\alpha^{1}_{0,1}`|:math:`\alpha^{1}_{0,2}`| |
-+------------------------+------------------------+ |
-|:math:`\alpha^{2}_{0,1}`|:math:`\alpha^{2}_{0,2}`| |
-+------------------------+------------------------+------------------+
-|:math:`\alpha^{0}_{1,0}`|:math:`\alpha^{0}_{1,2}`|Coefficients |
-+------------------------+------------------------+for SVs of class 1|
-|:math:`\alpha^{1}_{1,0}`|:math:`\alpha^{1}_{1,2}`| |
-+------------------------+------------------------+------------------+
-|:math:`\alpha^{0}_{2,0}`|:math:`\alpha^{0}_{2,1}`|Coefficients |
-+------------------------+------------------------+for SVs of class 2|
-|:math:`\alpha^{1}_{2,0}`|:math:`\alpha^{1}_{2,1}`| |
-+------------------------+------------------------+------------------+
++------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
+|:math:`\alpha^{0}_{0,1}`|:math:`\alpha^{1}_{0,1}`|:math:`\alpha^{2}_{0,1}`|:math:`\alpha^{0}_{1,0}`|:math:`\alpha^{1}_{1,0}`|:math:`\alpha^{0}_{2,0}`|:math:`\alpha^{1}_{2,0}`|
++------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
+|:math:`\alpha^{0}_{0,2}`|:math:`\alpha^{1}_{0,2}`|:math:`\alpha^{2}_{0,2}`|:math:`\alpha^{0}_{1,2}`|:math:`\alpha^{1}_{1,2}`|:math:`\alpha^{0}_{2,1}`|:math:`\alpha^{1}_{2,1}`|
++------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
+|Coefficients |Coefficients |Coefficients |
+|for SVs of class 0 |for SVs of class 1 |for SVs of class 2 |
++--------------------------------------------------------------------------+-------------------------------------------------+-------------------------------------------------+
.. topic:: Examples:
