Fix spelling errors in svm doc.

Add a bit of doc.

From: Fabian Pedregosa <fabian.pedregosa@inria.fr>

git-svn-id: https://scikit-learn.svn.sourceforge.net/svnroot/scikit-learn/trunk@564 22fbfee3-77ab-4535-9bad-27d1bd3bc7d8

doc/modules/svm.rst

@@ -34,6 +34,13 @@ non-linear and the transformed space high dimensional; thus though the
 classifier is a hyperplane in the high-dimensional feature space, it
 may be non-linear in the original input space.
 
+The decision function in this case will be:
+
+.. math:: sgn(\sum_{i=1}^l \alpha_i K(x_i, x) + \rho)
+
+where :math:`\alpha, \rho` can be accessed through fields support_ and
+rho_ of the classifier instance, respectevely.
+
 If the kernel used is a Gaussian radial basis function, the
 corresponding feature space is a Hilbert space of infinite
 dimension. Maximum margin classifiers are well regularized, so the
@@ -41,10 +48,9 @@ infinite dimension does not spoil the results. Available kernels are,
 
   * linear :math:`(1 + <x, x'>)`
   * polynomial :math:`(1 + <x, x'>)^d`
-  * radial :math:`exp(-\gamma |x-x'|^2)`
+  * radial basis :math:`exp(-\gamma |x-x'|^2)`
   * sigmoid :math:`tanh(x_i x_j + c)`
 
-
 The exclusive-OR is the simplest problem that cannot be solved using a
 linear kernel. In this problem, point (x, y) belongs has target 1 if
 and only if x > 0 XOR y > 0. In the following example, we create a
@@ -80,7 +86,7 @@ data close to the model prediction.
 
 Distribution estimation
 =======================
-One-class SVM is used for outlayer detection, that is, given a set of
+One-class SVM is used for out-layer detection, that is, given a set of
 samples, it will detect the soft boundary of that set.
 
 .. linteralinclude:: ../../examples/plot_svm_oneclass.py
@@ -91,71 +97,28 @@ samples, it will detect the soft boundary of that set.
 
 Scaling
 =======
+Support Vector Machine algorithms are not scale-invariant, so it is
+highly recommended to standarize the input vector X to have mean 0 and
+variance 1. Note that the *same* scaling must be applied to the test
+vector to obtain meaningful results.
 
-TODO
-
-.. Mathematical formulation (Model selection)
-.. ========================
-
-
-.. C-support vector classification (C-SVC)
-.. ---------------------------------------
-.. Given training vectors :math:`x_i \in \mathbb{R}^n , i=1, ..., l` in
-.. two classes, and a vector :math:`y \in \mathbb{R}^l` such that
-.. :math:`y_i \in {1, -1}`, C-SVC solves the following primal problem:
-
-.. .. math:: \min_{w, b, \xi} {1 \over 2} w^T w + C \sum_{i=1}^l \xi_i
-.. .. math:: \textrm{subject to}\ y_i (w^T \phi(x_i) + b) \geq 1 - \xi_i
-.. .. math:: \xi_i >= 0, i=1, .., l
-
-.. Here training vectors :math:`x_i` are mapped into a higher (maybe
-.. infinite) dimensional space by the function :math:`phi`. The decision
-.. function is
-
-.. .. math::    sgn(\sum_{i=0}^l y_i \alpha_i K(x_i, x) + b)
-
-.. This is implemented in class SVC
-
+See `The CookBook
+<https://sourceforge.net/apps/trac/scikit-learn/wiki/CookBook>` for
+some examples on scaling.
 
-.. Nu-Support Vector Classification
-.. --------------------------------
-.. The nu-Support Vector Classification uses a new parameter :math:`\nu`
-.. which controls the number of support vectors and trainign errors. The
-.. parameter :math:`nu \in (0, 1]` is an upper bound on the fraction of
-.. training errors and a lower bound of the fraction of support vectors.
 
-.. Given training vectors :math:`x_i \in \mathbb{R}^n , i=1, ..., l` in
-.. two classes, and a vector :math:`y \in \mathbb{R}^l` such that
-.. :math:`y_i \in {1, -1}`, C-SVC solves the following primal problem:
-
-.. .. math:: \min_{w, b, \xi} {1 \over 2} w^T w - \nu \rho + {1 \over 2} \sum_{i=1}^l \xi_i
-
-..           \textrm{subject to}\ y_i (w^T \phi(x_i) + b) \geq \rho - \xi_i
-
-..           \xi_i \geq 0, i=1, .., l, \rho \geq 0
-
-.. The decision function is:
-
-.. .. math::    sgn(\sum_{i=1}^l y_i \alpha_i K(x_i, x) + b
-
-.. This is implemented in SVC(impl='nu-svc')
-
-
-
-Low-level implementation
-========================
-
-Internally, we use libsvm[1] to handle all computations. Libsvm is binded
-through some wrappers written in C and Cython.
+Implementation details
+======================
+Internally, we use libsvm[1] to handle all computations. Libsvm is wrapped
+using C and Cython.
 
 .. [1] http://www.csie.ntu.edu.tw/~cjlin/libsvm/
 
 
 References
 ==========
-
 For a description of the implementation and details of the algorithms
 used, please refer to
-http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf
 
-http://en.wikipedia.org/wiki/Support_vector_machine
+    - http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf
+    - http://en.wikipedia.org/wiki/Support_vector_machine