Python Machine Learning - Code Examples

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 -p numpy,pandas,matplotlib,sklearn
Sebastian Raschka 
last updated: 2017-03-10 

numpy 1.12.0
pandas 0.19.2
matplotlib 2.0.0
sklearn 0.18.1

The use of watermark is optional. You can install this IPython extension via "pip install watermark". For more information, please see: https://github.com/rasbt/watermark.

Overview





In [2]:
from IPython.display import Image
%matplotlib inline
In [3]:
# Added version check for recent scikit-learn 0.18 checks
from distutils.version import LooseVersion as Version
from sklearn import __version__ as sklearn_version

Choosing a classification algorithm

...

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 [4]:
from sklearn import datasets
import numpy as np

iris = datasets.load_iris()
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 [5]:
if Version(sklearn_version) < '0.18':
    from sklearn.cross_validation import train_test_split
else:
    from sklearn.model_selection 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 [6]:
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 [7]:
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[7]:
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 [8]:
y_test.shape
Out[8]:
(45,)
In [9]:
y_pred = ppn.predict(X_test_std)
print('Misclassified samples: %d' % (y_test != y_pred).sum())
Misclassified samples: 4
In [10]:
from sklearn.metrics import accuracy_score

print('Accuracy: %.2f' % accuracy_score(y_test, y_pred))
Accuracy: 0.91
In [11]:
from matplotlib.colors import ListedColormap
import matplotlib.pyplot as plt
import warnings


def versiontuple(v):
    return tuple(map(int, (v.split("."))))


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())

    for idx, cl in enumerate(np.unique(y)):
        plt.scatter(x=X[y == cl, 0], 
                    y=X[y == cl, 1],
                    alpha=0.6, 
                    c=cmap(idx),
                    edgecolor='black',
                    marker=markers[idx], 
                    label=cl)

    # highlight test samples
    if test_idx:
        # plot all samples
        if not versiontuple(np.__version__) >= versiontuple('1.9.0'):
            X_test, y_test = X[list(test_idx), :], y[list(test_idx)]
            warnings.warn('Please update to NumPy 1.9.0 or newer')
        else:
            X_test, y_test = X[test_idx, :], y[test_idx]

        plt.scatter(X_test[:, 0],
                    X_test[:, 1],
                    c='',
                    alpha=1.0,
                    edgecolor='black',
                    linewidths=1,
                    marker='o',
                    s=55, label='test set')

Training a perceptron model using the standardized training data:

In [12]:
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 [13]:
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 [14]:
Image(filename='./images/03_03.png', width=500) 
Out[14]:



Learning the weights of the logistic cost function

In [15]:
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 [16]:
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 [17]:
if Version(sklearn_version) < '0.17':
    lr.predict_proba(X_test_std[0, :])
else:
    lr.predict_proba(X_test_std[0, :].reshape(1, -1))



Tackling overfitting via regularization

In [18]:
Image(filename='./images/03_06.png', width=700) 
Out[18]:
In [19]:
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 [20]:
Image(filename='./images/03_07.png', width=700) 
Out[20]:

Maximum margin intuition

...

Dealing with the nonlinearly separable case using slack variables

In [21]:
Image(filename='./images/03_08.png', width=600) 
Out[21]:
In [22]:
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()

Alternative implementations in scikit-learn



Solving non-linear problems using a kernel SVM

In [23]:
import matplotlib.pyplot as plt
import numpy as np

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 [24]:
Image(filename='./images/03_11.png', width=700) 
Out[24]: