# Chapter 3 - A Tour of Machine Learning Classifiers Using Scikit-Learn¶

Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s).

In [1]:
%load_ext watermark
%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scikit-learn

Sebastian Raschka
Last updated: 08/21/2015

CPython 3.4.3
IPython 3.2.1

numpy 1.9.2
pandas 0.16.2
matplotlib 1.4.3
scikit-learn 0.16.1

In [2]:
# to install watermark just uncomment the following line:
#%install_ext https://raw.githubusercontent.com/rasbt/watermark/master/watermark.py


### Overview¶

In [1]:
from IPython.display import Image


...

# First steps with scikit-learn¶

Loading the Iris dataset from scikit-learn. Here, the third column represents the petal length, and the fourth column the petal width of the flower samples. The classes are already converted to integer labels where 0=Iris-Setosa, 1=Iris-Versicolor, 2=Iris-Virginica.

In [3]:
from sklearn import datasets
import numpy as np

X = iris.data[:, [2, 3]]
y = iris.target

print('Class labels:', np.unique(y))

Class labels: [0 1 2]


Splitting data into 70% training and 30% test data:

In [4]:
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)


Standardizing the features:

In [5]:
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)


## Training a perceptron via scikit-learn¶

Redefining the plot_decision_region function from chapter 2:

In [6]:
from sklearn.linear_model import Perceptron

ppn = Perceptron(n_iter=40, eta0=0.1, random_state=0)
ppn.fit(X_train_std, y_train)

Out[6]:
Perceptron(alpha=0.0001, class_weight=None, eta0=0.1, fit_intercept=True,
n_iter=40, n_jobs=1, penalty=None, random_state=0, shuffle=True,
verbose=0, warm_start=False)
In [7]:
y_test.shape

Out[7]:
(45,)
In [8]:
y_pred = ppn.predict(X_test_std)
print('Misclassified samples: %d' % (y_test != y_pred).sum())

Misclassified samples: 4

In [9]:
from sklearn.metrics import accuracy_score

print('Accuracy: %.2f' % accuracy_score(y_test, y_pred))

Accuracy: 0.91

In [10]:
from matplotlib.colors import ListedColormap
import matplotlib.pyplot as plt
%matplotlib inline

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')


Training a perceptron model using the standardized training data:

In [11]:
%matplotlib inline

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.tight_layout()
# plt.savefig('./figures/iris_perceptron_scikit.png', dpi=300)
plt.show()


# Modeling class probabilities via logistic regression¶

...

### Logistic regression intuition and conditional probabilities¶

In [12]:
%matplotlib inline
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.ylim(-0.1, 1.1)
plt.xlabel('z')
plt.ylabel('$\phi (z)$')

# y axis ticks and gridline
plt.yticks([0.0, 0.5, 1.0])
ax = plt.gca()
ax.yaxis.grid(True)

plt.tight_layout()
# plt.savefig('./figures/sigmoid.png', dpi=300)
plt.show()

In [5]:
Image(filename='./images/03_03.png', width=500)

Out[5]:

### Learning the weights of the logistic cost function¶

In [13]:
def cost_1(z):
return - np.log(sigmoid(z))

def cost_0(z):
return - np.log(1 - sigmoid(z))

z = np.arange(-10, 10, 0.1)
phi_z = sigmoid(z)

c1 = [cost_1(x) for x in z]
plt.plot(phi_z, c1, label='J(w) if y=1')

c0 = [cost_0(x) for x in z]
plt.plot(phi_z, c0, linestyle='--', label='J(w) if y=0')

plt.ylim(0.0, 5.1)
plt.xlim([0, 1])
plt.xlabel('$\phi$(z)')
plt.ylabel('J(w)')
plt.legend(loc='best')
plt.tight_layout()
# plt.savefig('./figures/log_cost.png', dpi=300)
plt.show()


### Training a logistic regression model with scikit-learn¶

In [14]:
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.tight_layout()
# plt.savefig('./figures/logistic_regression.png', dpi=300)
plt.show()

In [15]:
lr.predict_proba(X_test_std[0,:])

Out[15]:
array([[  2.05743774e-11,   6.31620264e-02,   9.36837974e-01]])

### Tackling overfitting via regularization¶

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Image(filename='./images/03_06.png', width=700)

Out[3]:
In [16]:
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.savefig('./figures/regression_path.png', dpi=300)
plt.show()


# Maximum margin classification with support vector machines¶

In [5]:
Image(filename='./images/03_07.png', width=700)

Out[5]:

...

## Dealing with the nonlinearly separable case using slack variables¶

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Image(filename='./images/03_08.png', width=600)

Out[8]:
In [17]:
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.tight_layout()
# plt.savefig('./figures/support_vector_machine_linear.png', dpi=300)
plt.show()


# Solving non-linear problems using a kernel SVM¶

In [18]:
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline

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.xlim([-3, 3])
plt.ylim([-3, 3])
plt.legend(loc='best')
plt.tight_layout()
# plt.savefig('./figures/xor.png', dpi=300)
plt.show()

In [9]:
Image(filename='./images/03_11.png', width=700)

Out[9]: