adding example that illustrates that L1 penalty leads to sparse estimates of coef_

git-svn-id: https://scikit-learn.svn.sourceforge.net/svnroot/scikit-learn/trunk@697 22fbfee3-77ab-4535-9bad-27d1bd3bc7d8

examples/plot_logistic_l1_l2_coef.py

+# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
+# License: BSD Style.
+
+# $Id$
+
+import numpy as np
+
+from scikits.learn.logistic import LogisticRegression
+from scikits.learn import datasets
+
+iris = datasets.load_iris()
+X = iris.data
+y = iris.target
+
+# Set regularization parameter
+C = 0.1
+
+classifier_l1_LR = LogisticRegression(C=C, penalty='l1')
+classifier_l2_LR = LogisticRegression(C=C, penalty='l2')
+classifier_l1_LR.fit(X, y)
+classifier_l2_LR.fit(X, y)
+
+hyperplane_coefficients_l1_LR = classifier_l1_LR.coef_[:]
+hyperplane_coefficients_l2_LR = classifier_l2_LR.coef_[:]
+
+# hyperplane_coefficients_l1_LR contains zeros due to the
+# L1 sparsity inducing norm
+
+pct_non_zeros_l1_LR = np.mean(hyperplane_coefficients_l1_LR != 0) * 100
+pct_non_zeros_l2_LR = np.mean(hyperplane_coefficients_l2_LR != 0) * 100
+
+print "Percentage of non zeros coefficients (L1) : %f" % pct_non_zeros_l1_LR
+print "Percentage of non zeros coefficients (L2) : %f" % pct_non_zeros_l2_LR