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#!/usr/bin/python

''' decision_tree.py shows three impurity measures Gini, entropy, and

misclassification error when used with a decision tree classifier.

These measures are used to estimate the information gain at each split.

1) plot the 3 kinds of impurity measure

2) run the decision tree on the e13b data and plot the decision regions

To create a drawing of the tree run:

dot -Tpng tree.dot -o tree.png

Created on Jun 23, 2016

from Python Machine Learning by Sebastian Raschka under the following license

The MIT License (MIT)

Permission is hereby granted, free of charge, to any person obtaining a copy

of this software and associated documentation files (the "Software"), to deal

in the Software without restriction, including without limitation the rights

to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

copies of the Software, and to permit persons to whom the Software is

furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all

copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

SOFTWARE.

@author: richard lyman

'''

import numpy as np

import ocr_utils

import matplotlib.pyplot as plt

from sklearn.preprocessing import StandardScaler

y_train, X_train, y_test, X_test, labels = ocr_utils.load_E13B(chars_to_train = (48,49,50) , columns=(9,17), test_size=0.3, nChars=300, random_state=0)

def gini(p):

return (p)*(1 - (p)) + (1-p)*(1 - (1-p))

def entropy(p):

return - p*np.log2(p) - (1 - p)*np.log2((1 - p))

def error(p):

return 1 - np.max([p, 1 - p])

x = np.arange(0.0, 1.0, 0.01)

ent = [entropy(p) if p != 0 else None for p in x]

sc_ent = [e*0.5 if e else None for e in ent]

err = [error(i) for i in x]

fig = plt.figure()

ax = plt.subplot(111)

for i, lab, ls, c, in zip([ent, sc_ent, gini(x), err],

['Entropy', 'Entropy (scaled)',

'Gini Impurity', 'Misclassification Error'],

['-', '-', '--', '-.'],

['black', 'lightgray', 'red', 'green', 'cyan']):

line = ax.plot(x, i, label=lab, linestyle=ls, lw=2, color=c)

ax.legend(loc='upper center', ncol=2, fancybox=True, shadow=False)

ax.axhline(y=0.5, linewidth=1, color='k', linestyle='--')

ax.axhline(y=1.0, linewidth=1, color='k', linestyle='--')

plt.ylim([0, 1.2])

plt.xlabel('p(i=1)')

plt.ylabel('Impurity Index')

plt.tight_layout()

title='impurity'

plt.title(title)

ocr_utils.show_figures(plt,title=title)

sc = StandardScaler()

sc.fit(X_train)

X_train_std = sc.transform(X_train)

X_test_std = sc.transform(X_test)

X_combined_std = np.vstack((X_train_std, X_test_std))

y_combined = np.hstack((y_train, y_test))

from sklearn.tree import DecisionTreeClassifier

tree = DecisionTreeClassifier(criterion='entropy', max_depth=3, random_state=0)

tree.fit(X_train, y_train)

X_combined = np.vstack((X_train, X_test))

y_combined = np.hstack((y_train, y_test))

ocr_utils.plot_decision_regions(X=X_combined,

y=y_combined,

classifier=tree,

test_idx=range(len(X_test),len(X_combined)),

labels=labels,

title='decision tree entropy')

from sklearn.ensemble import RandomForestClassifier

forest = RandomForestClassifier(criterion='entropy',

n_estimators=10,

random_state=1,

n_jobs=2)

forest.fit(X_train, y_train)

ocr_utils.plot_decision_regions(X=X_combined,

y=y_combined,

classifier=forest,

labels=labels,

test_idx=range(len(X_test_std),len(X_combined_std)),

title='random_forest')

print ('\n########################### No Errors ####################################')