More doc for the svm module.

Added a little reference for OneClassSVM and some examples.

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

git-svn-id: https://scikit-learn.svn.sourceforge.net/svnroot/scikit-learn/trunk@563 22fbfee3-77ab-4535-9bad-27d1bd3bc7d8

doc/modules/svm.rst

@@ -80,16 +80,14 @@ data close to the model prediction.
 
 Distribution estimation
 =======================
-One-class SVM was proposed by Scholkopf et al. (2001) for estimating
-the support of a high-dimensional distribution. Given training vectors
-:math:`x_i \in \mathbb{R}^n, i=1, .., l` without any class
-information, the primal form is:
+One-class SVM is used for outlayer detection, that is, given a set of
+samples, it will detect the soft boundary of that set.
 
-.. math::    \min_{w, b, \xi} {1 \over 2} w^T w - \rho + {1 \over \nu l} \sum_{i=1}^l \xi_i
+.. linteralinclude:: ../../examples/plot_svm_oneclass.py
 
-             \textrm{subject to} w^T \phi(x_i) \geq \rho - \xi_i
+.. image:: data_svm/oneclass.png
 
-             \xi_i \geq 0, i=1,...,l
+.. autoclass:: scikits.learn.svm.OneClassSVM
 
 Scaling
 =======

examples/plot_svm_hyperplane.py

@@ -13,12 +13,22 @@ clf.fit(X, Y)
 
 # get the separating hyperplane
 w = np.dot(clf.coef_[0], clf.support_) 
-xx = np.linspace(-2, 2)
-yy = (clf.rho_[0] - w[0]*xx)/w[1]
+a = -w[0]/w[1]
+xx = np.linspace(-5, 5)
+yy = a*xx + (clf.rho_[0])/w[1]
+
+# plot the paralels to the separating hyperplane that pass through the
+# support vectors
+b = clf.support_[0]
+yy_down = a*xx + (b[1] - a*b[0])
+b = clf.support_[-1]
+yy_up = a*xx + (b[1] - a*b[0])
 
 # plot the line, the points, and the nearest vectors to the plane
 pl.set_cmap(pl.cm.Paired)
-pl.plot(xx, yy, 'k--')
+pl.plot(xx, yy, 'k-')
+pl.plot(xx, yy_down, 'k--')
+pl.plot(xx, yy_up, 'k--')
 pl.scatter(X[:,0], X[:,1], c=Y)
 pl.scatter(clf.support_[:,0], clf.support_[:,1], marker='+')
 

examples/plot_svm_nonlinear.py

@@ -3,7 +3,8 @@ import numpy as np
 import pylab as pl
 from scikits.learn import svm
 
-xx, yy = np.meshgrid(np.linspace(-5, 5), np.linspace(-5, 5))
+xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))
+np.random.seed(0)
 X = np.random.randn(300, 2)
 Y = np.logical_xor(X[:,0]>0, X[:,1]>0)
 

examples/plot_svm_oneclass.py

+
+import numpy as np
+import pylab as pl
+from scikits.learn import svm
+
+xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))
+X = np.random.randn(100, 2)
+Y = [0]*100
+
+# fit the model
+clf = svm.OneClassSVM(nu=0.5)
+clf.fit(X, Y)
+
+# plot the line, the points, and the nearest vectors to the plane
+Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
+Z = Z.reshape(xx.shape)
+
+pl.set_cmap(pl.cm.Paired)
+pl.pcolormesh(xx, yy, Z)
+pl.scatter(X[:,0], X[:,1], c=Y)
+pl.scatter(clf.support_[:,0], clf.support_[:,1], c='black')
+pl.axis('tight')
+pl.show()