-- Choosing a classification algorithm
1.Selection of features.
2.Choosing a performance metric.
3.Choosing a classifier and optimization algorithm.
4.Evaluating the performance of the model.
5.Tuning the algorithm.
-- First steps with scikit-learn
Training a perceptron via scikit-learn
from sklearn import datasets
import numpy as np
iris = datasets.load_iris()
X = iris.data[:, [2, 3]]
y = iris.target
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0)
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
sc.fit(X_train)
X_train_std = sc.transform(X_train)
X_test_std = sc.transform(X_test)
from sklearn.linear_model import Perceptron
ppn = Perceptron(n_iter=40, eta0=0.1, random_state=0)
ppn.fit(X_train_std, y_train)
y_pred = ppn.predict(X_test_std)
print('Misclassified samples: %d' % (y_test != y_pred).sum())
from sklearn.metrics import accuracy_score
print('Accuracy: %.2f' % accuracy_score(y_test, y_pred))
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from matplotlib.colors import ListedColormap
import matplotlib.pyplot as plt
def plot_decision_regions(X, y, classifier,
test_idx=None, resolution=0.02):
# setup marker generator and color map
markers = ('s', 'x', 'o', '^', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
np.arange(x2_min, x2_max, resolution))
Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
Z = Z.reshape(xx1.shape)
plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
plt.xlim(xx1.min(), xx1.max())
plt.ylim(xx2.min(), xx2.max())
# plot all samples
X_test, y_test = X[test_idx, :], y[test_idx]
for idx, cl in enumerate(np.unique(y)):
plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],
alpha=0.8, c=cmap(idx),
marker=markers[idx], label=cl)
# highlight test samples
if test_idx:
X_test, y_test = X[test_idx, :], y[test_idx]
plt.scatter(X_test[:, 0], X_test[:, 1], c='',
alpha=1.0, linewidth=1, marker='o',
s=55, label='test set')
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X_combined_std = np.vstack((X_train_std, X_test_std))
y_combined = np.hstack((y_train, y_test))
plot_decision_regions(X=X_combined_std,
y=y_combined,
classifier=ppn,
test_idx=range(105,150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.legend(loc='upper left')
plt.show()
-- Modeling class probabilities via logistic regression
-- Logistic regression intuition and conditional probabilities
import matplotlib.pyplot as plt
import numpy as np
def sigmoid(z):
... return 1.0 / (1.0 + np.exp(-z))
z = np.arange(-7, 7, 0.1)
phi_z = sigmoid(z)
plt.plot(z, phi_z)
plt.axvline(0.0, color='k')
plt.axhspan(0.0, 1.0, facecolor='1.0', alpha=1.0, ls='dotted')
plt.axhline(y=0.5, ls='dotted', color='k')
plt.yticks([0.0, 0.5, 1.0])
plt.ylim(-0.1, 1.1)
plt.xlabel('z')
plt.ylabel('$\phi (z)$')
plt.show()
-- Learning the weights of the logistic cost function
-- Training a logistic regression model with scikit-learn
from sklearn.linear_model import LogisticRegression
lr = LogisticRegression(C=1000.0, random_state=0)
lr.fit(X_train_std, y_train)
plot_decision_regions(X_combined_std,
y_combined, classifier=lr,
test_idx=range(105,150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.legend(loc='upper left')
plt.show()
lr.predict_proba(X_test_std[0,:])
weights, params = [], []
for c in np.arange(-5, 5):
lr = LogisticRegression(C=10**c, random_state=0)
lr.fit(X_train_std, y_train)
weights.append(lr.coef_[1])
params.append(10**c)
weights = np.array(weights)
plt.plot(params, weights[:, 0],
label='petal length')
plt.plot(params, weights[:, 1], linestyle='--',
label='petal width')
plt.ylabel('weight coefficient')
plt.xlabel('C')
plt.legend(loc='upper left')
plt.xscale('log')
plt.show()
lr.predict_proba(X_test_std[0,:])
-- Tackling overfitting via regularization
weights, params = [], []
for c in np.arange(-5, 5):
lr = LogisticRegression(C=10**c, random_state=0)
lr.fit(X_train_std, y_train)
weights.append(lr.coef_[1])
params.append(10**c)
weights = np.array(weights)
plt.plot(params, weights[:, 0],
label='petal length')
plt.plot(params, weights[:, 1], linestyle='--',
label='petal width')
plt.ylabel('weight coefficient')
plt.xlabel('C')
plt.legend(loc='upper left')
plt.xscale('log')
plt.show()
-- Maximum margin classification with support vector machines
Maximum margin intuition
-- Dealing with the nonlinearly separable case using slack variables
from sklearn.svm import SVC
svm = SVC(kernel='linear', C=1.0, random_state=0)
svm.fit(X_train_std, y_train)
plot_decision_regions(X_combined_std,
y_combined, classifier=svm,
test_idx=range(105,150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.legend(loc='upper left')
plt.show()
-- Alternative implementations in scikit-learn
from sklearn.linear_model import SGDClassifier
ppn = SGDClassifier(loss='perceptron')
lr = SGDClassifier(loss='log')
svm = SGDClassifier(loss='hinge')
-- Solving nonlinear problems using a kernel SVM
np.random.seed(0)
X_xor = np.random.randn(200, 2)
y_xor = np.logical_xor(X_xor[:, 0] > 0, X_xor[:, 1] > 0)
y_xor = np.where(y_xor, 1, -1)
plt.scatter(X_xor[y_xor==1, 0], X_xor[y_xor==1, 1],
c='b', marker='x', label='1')
plt.scatter(X_xor[y_xor==-1, 0], X_xor[y_xor==-1, 1],
c='r', marker='s', label='-1')
plt.ylim(-3.0)
plt.legend()
plt.show()
-- Using the kernel trick to find separating hyperplanes in higher dimensional space
svm = SVC(kernel='rbf', random_state=0, gamma=0.10, C=10.0)
svm.fit(X_xor, y_xor)
plot_decision_regions(X_xor, y_xor, classifier=svm)
plt.legend(loc='upper left')
plt.show()
svm = SVC(kernel='rbf', random_state=0, gamma=100.0, C=1.0)
svm.fit(X_train_std, y_train)
plot_decision_regions(X_combined_std,
y_combined, classifier=svm,
test_idx=range(105,150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.legend(loc='upper left')
plt.show()
--- Decision tree learning
--- Maximizing information gain ñ getting the most bang for the buck
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import matplotlib.pyplot as plt
import numpy as np
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', bbox_to_anchor=(0.5, 1.15),
ncol=3, 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, 1.1])
plt.xlabel('p(i=1)')
plt.ylabel('Impurity Index')
plt.show()
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--- Building a decision tree
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))
plot_decision_regions(X_combined, y_combined,
classifier=tree, test_idx=range(105,150))
plt.xlabel('petal length [cm]')
plt.ylabel('petal width [cm]')
plt.legend(loc='upper left')
plt.show()
from sklearn.tree import export_graphviz
export_graphviz(tree,
out_file='tree.dot',
feature_names=['petal length', 'petal width'])
dot -Tpng tree.dot -o tree.png
--- Combining weak to strong learners via random forests
from sklearn.ensemble import RandomForestClassifier
forest = RandomForestClassifier(criterion='entropy',
n_estimators=10,
random_state=1,
n_jobs=2)
forest.fit(X_train, y_train)
plot_decision_regions(X_combined, y_combined,
classifier=forest, test_idx=range(105,150))
plt.xlabel('petal length')
plt.ylabel('petal width')
plt.legend(loc='upper left')
plt.show()
--- K-nearest neighbors ñ a lazy learning algorithm
from sklearn.neighbors import KNeighborsClassifier
knn = KNeighborsClassifier(n_neighbors=5, p=2,
metric='minkowski')
knn.fit(X_train_std, y_train)
plot_decision_regions(X_combined_std, y_combined,
classifier=knn, test_idx=range(105,150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.show()
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