
from sklearn.neural_network import MLPClassifier
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
from matplotlib.colors import ListedColormap
import numpy as np
import matplotlib.pyplot as plt

X, y = make_moons(n_samples=100, noise=0.25, random_state=3)

X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)


# default = 100 hidden nodes and activation='relu'
mlp = MLPClassifier(solver='lbfgs', random_state=0).fit(X_train, y_train)

plot_2d_separator(mlp, X_train) # huplfunctie verborgen in deze notebook
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, 
            cmap=ListedColormap(['#0000aa', '#ff2020']))

<matplotlib.collections.PathCollection at 0x18cd658e430>


# 10 nodes in 1 hidden layer ...

mlp = MLPClassifier(solver='lbfgs', random_state=0, 
                    hidden_layer_sizes=[10]).fit(X_train, y_train)

C:\ProgramData\Anaconda3\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:541: ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.

Increase the number of iterations (max_iter) or scale the data as shown in:
    https://scikit-learn.org/stable/modules/preprocessing.html
  self.n_iter_ = _check_optimize_result("lbfgs", opt_res, self.max_iter)


# 10 nodes in 1 hidden layer ...
# ... resulteren in een decision boundary van 10 lijnsegmenten

mlp = MLPClassifier(solver='lbfgs', random_state=0, hidden_layer_sizes=[10],
                    max_iter=300).fit(X_train, y_train)

plot_2d_separator(mlp, X_train) # huplfunctie verborgen in deze notebook
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=ListedColormap(['#0000aa', '#ff2020']))

<matplotlib.collections.PathCollection at 0x18cd1e90940>


# laat ons een 2de laag toevoegen ...

mlp = MLPClassifier(solver='lbfgs', random_state=0, 
                    hidden_layer_sizes=[10,10]).fit(X_train, y_train)

plot_2d_separator(mlp, X_train) # huplfunctie verborgen in deze notebook
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=ListedColormap(['#0000aa', '#ff2020']))

<matplotlib.collections.PathCollection at 0x18cd1ee8160>


# en laat ons de activatiefunctie veranderen naar tanh ...

mlp = MLPClassifier(solver='lbfgs', activation='tanh', random_state=0,
                    max_iter=300,
                    hidden_layer_sizes=[10,10]).fit(X_train, y_train)

plot_2d_separator(mlp, X_train) # huplfunctie verborgen in deze notebook
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=ListedColormap(['#0000aa', '#ff2020']))

<matplotlib.collections.PathCollection at 0x18cd1f2bb50>


from sklearn.datasets import load_breast_cancer
cancer = load_breast_cancer()

X_train, X_test, y_train, y_test = train_test_split(
    cancer.data, cancer.target, random_state=0)

mlp = MLPClassifier(random_state=0)
mlp.fit(X_train, y_train)

print("Accuracy on training set: {:.2f}".format(mlp.score(X_train, y_train)))
print("Accuracy on test set: {:.2f}".format(mlp.score(X_test, y_test)))

Accuracy on training set: 0.93
Accuracy on test set: 0.93


print("Cancer data per-feature maxima:\n{}".format(cancer.data.max(axis=0)))

Cancer data per-feature maxima:
[2.811e+01 3.928e+01 1.885e+02 2.501e+03 1.634e-01 3.454e-01 4.268e-01
 2.012e-01 3.040e-01 9.744e-02 2.873e+00 4.885e+00 2.198e+01 5.422e+02
 3.113e-02 1.354e-01 3.960e-01 5.279e-02 7.895e-02 2.984e-02 3.604e+01
 4.954e+01 2.512e+02 4.254e+03 2.226e-01 1.058e+00 1.252e+00 2.910e-01
 6.638e-01 2.075e-01]


# compute the mean value per feature on the training set
mean_on_train = X_train.mean(axis=0)
# compute the standard deviation of each feature on the training set
std_on_train = X_train.std(axis=0)

# subtract the mean, and scale by inverse standard deviation
# afterward, mean=0 and std=1
X_train_scaled = (X_train - mean_on_train) / std_on_train
# use THE SAME transformation (using training mean and std) on the test set
X_test_scaled = (X_test - mean_on_train) / std_on_train

mlp = MLPClassifier(random_state=0)
mlp.fit(X_train_scaled, y_train)

print("Accuracy on training set: {:.3f}".format(
    mlp.score(X_train_scaled, y_train)))
print("Accuracy on test set: {:.3f}".format(mlp.score(X_test_scaled, y_test)))

Accuracy on training set: 0.991
Accuracy on test set: 0.965

C:\ProgramData\Anaconda3\lib\site-packages\sklearn\neural_network\_multilayer_perceptron.py:686: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.
  warnings.warn(


# laat ons het aantal iteraties dus verhogen ....

mlp = MLPClassifier(max_iter=1000, random_state=0)
mlp.fit(X_train_scaled, y_train)

print("Accuracy on training set: {:.3f}".format(
    mlp.score(X_train_scaled, y_train)))
print("Accuracy on test set: {:.3f}".format(mlp.score(X_test_scaled, y_test)))

# sterk resultaat !!

Accuracy on training set: 1.000
Accuracy on test set: 0.972


plt.figure(figsize=(20, 5))
plt.imshow(mlp.coefs_[0], interpolation='none', cmap='viridis')
plt.yticks(range(30), cancer.feature_names)
plt.xlabel("Columns in weight matrix")
plt.ylabel("Input feature")
plt.colorbar()

<matplotlib.colorbar.Colorbar at 0x18cd20178e0>

Neurale netwerken¶

K. Verbeeck, T. Van den Bossche, J. Maervoet¶

1. Inleiding artificiële neurale netwerken (ANN)¶

Typische kenmerken ANN¶

Activatiefunctie¶

Deep Learning¶

Situering ANN¶

2. Perceptron¶

Gebruik perceptron voor voorspellingen¶

Leeralgoritme voor het trainingsproces¶

Grafische voorstelling¶

Belangrijke eigenschappen (1)¶

Belangrijke eigenschappen (2)¶

3. Multi-Layer Perceptron (MLP)¶

Backpropagation¶

Decision boundary¶

MLPs in scikit (docs)¶

Demo parameter-tuning¶

Regularisatie met de α-parameter

Gevoeligheid t.o.v. de keuze van de random startgewichten¶

Vergeet niet om je data te scalen¶

Visualisatie gewichten¶

Besluit¶

Bronnen en links¶