113 lines
4.0 KiB
Python
113 lines
4.0 KiB
Python
"""
|
|
================================================
|
|
Varying regularization in Multi-layer Perceptron
|
|
================================================
|
|
|
|
A comparison of different values for regularization parameter 'alpha' on
|
|
synthetic datasets. The plot shows that different alphas yield different
|
|
decision functions.
|
|
|
|
Alpha is a parameter for regularization term, aka penalty term, that combats
|
|
overfitting by constraining the size of the weights. Increasing alpha may fix
|
|
high variance (a sign of overfitting) by encouraging smaller weights, resulting
|
|
in a decision boundary plot that appears with lesser curvatures.
|
|
Similarly, decreasing alpha may fix high bias (a sign of underfitting) by
|
|
encouraging larger weights, potentially resulting in a more complicated
|
|
decision boundary.
|
|
"""
|
|
print(__doc__)
|
|
|
|
|
|
# Author: Issam H. Laradji
|
|
# License: BSD 3 clause
|
|
|
|
import numpy as np
|
|
from matplotlib import pyplot as plt
|
|
from matplotlib.colors import ListedColormap
|
|
from sklearn.model_selection import train_test_split
|
|
from sklearn.preprocessing import StandardScaler
|
|
from sklearn.datasets import make_moons, make_circles, make_classification
|
|
from sklearn.neural_network import MLPClassifier
|
|
|
|
h = .02 # step size in the mesh
|
|
|
|
alphas = np.logspace(-5, 3, 5)
|
|
names = ['alpha ' + str(i) for i in alphas]
|
|
|
|
classifiers = []
|
|
for i in alphas:
|
|
classifiers.append(MLPClassifier(alpha=i, random_state=1))
|
|
|
|
X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
|
|
random_state=0, n_clusters_per_class=1)
|
|
rng = np.random.RandomState(2)
|
|
X += 2 * rng.uniform(size=X.shape)
|
|
linearly_separable = (X, y)
|
|
|
|
datasets = [make_moons(noise=0.3, random_state=0),
|
|
make_circles(noise=0.2, factor=0.5, random_state=1),
|
|
linearly_separable]
|
|
|
|
figure = plt.figure(figsize=(17, 9))
|
|
i = 1
|
|
# iterate over datasets
|
|
for X, y in datasets:
|
|
# preprocess dataset, split into training and test part
|
|
X = StandardScaler().fit_transform(X)
|
|
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)
|
|
|
|
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
|
|
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
|
|
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
|
|
np.arange(y_min, y_max, h))
|
|
|
|
# just plot the dataset first
|
|
cm = plt.cm.RdBu
|
|
cm_bright = ListedColormap(['#FF0000', '#0000FF'])
|
|
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
|
|
# Plot the training points
|
|
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
|
|
# and testing points
|
|
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
|
|
ax.set_xlim(xx.min(), xx.max())
|
|
ax.set_ylim(yy.min(), yy.max())
|
|
ax.set_xticks(())
|
|
ax.set_yticks(())
|
|
i += 1
|
|
|
|
# iterate over classifiers
|
|
for name, clf in zip(names, classifiers):
|
|
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
|
|
clf.fit(X_train, y_train)
|
|
score = clf.score(X_test, y_test)
|
|
|
|
# Plot the decision boundary. For that, we will assign a color to each
|
|
# point in the mesh [x_min, x_max]x[y_min, y_max].
|
|
if hasattr(clf, "decision_function"):
|
|
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
|
|
else:
|
|
Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
|
|
|
|
# Put the result into a color plot
|
|
Z = Z.reshape(xx.shape)
|
|
ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)
|
|
|
|
# Plot also the training points
|
|
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright,
|
|
edgecolors='black', s=25)
|
|
# and testing points
|
|
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
|
|
alpha=0.6, edgecolors='black', s=25)
|
|
|
|
ax.set_xlim(xx.min(), xx.max())
|
|
ax.set_ylim(yy.min(), yy.max())
|
|
ax.set_xticks(())
|
|
ax.set_yticks(())
|
|
ax.set_title(name)
|
|
ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
|
|
size=15, horizontalalignment='right')
|
|
i += 1
|
|
|
|
figure.subplots_adjust(left=.02, right=.98)
|
|
plt.show()
|