13. Redes Neuronales

Datos

from sklearn.datasets import make_classification, make_blobs
# Conjunto de datos no separable
X_D2, y_D2 = make_blobs(n_samples = 100, n_features = 2, centers = 8,
                       cluster_std = 1.3, random_state = 4)

13.1. Funciones de activación

import numpy as np
import matplotlib.pyplot as plt
xrange = np.linspace(-2, 2, 200)

plt.figure(figsize=(7,6))

plt.plot(xrange, np.maximum(xrange, 0), label = 'relu')
plt.plot(xrange, np.tanh(xrange), label = 'tanh')
plt.plot(xrange, 1 / (1 + np.exp(-xrange)), label = 'logistic')
plt.legend()
plt.title('Funciones de activación para redes neuronales')
plt.xlabel('Input(x)')
plt.ylabel('Output: función de activación')

plt.show()

13.2. Una capa oculta

from sklearn.neural_network import MLPClassifier
from shared_utilities import plot_class_regions_for_classifier_subplot
from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X_D2, y_D2, random_state=0)

fig, subaxes = plt.subplots(3, 1, figsize=(6,18))

for units, axis in zip([1, 10, 100], subaxes):
    nnclf = MLPClassifier(hidden_layer_sizes = [units], solver='lbfgs',
                         random_state = 0).fit(X_train, y_train)
    
    title = 'Dataset 1: Red neuronal, 1 layer, {} nodo'.format(units)
    
    plot_class_regions_for_classifier_subplot(nnclf, X_train, y_train,
                                             X_test, y_test, title, axis)
    plt.tight_layout()

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

13.3. Dos capas ocultas

from shared_utilities import plot_class_regions_for_classifier

X_train, X_test, y_train, y_test = train_test_split(X_D2, y_D2, random_state=0)

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

plot_class_regions_for_classifier(nnclf, X_train, y_train, X_test, y_test,
                                 'Dataset 1: Red neuronal, 2 layers, 10/10 nodos')

13.3.1. Parámetro de regularización: alpha

X_train, X_test, y_train, y_test = train_test_split(X_D2, y_D2, random_state=0)

fig, subaxes = plt.subplots(4, 1, figsize=(6, 23))

for this_alpha, axis in zip([0.01, 0.1, 1.0, 5.0], subaxes):
    nnclf = MLPClassifier(solver='lbfgs', activation = 'tanh',
                         alpha = this_alpha,
                         hidden_layer_sizes = [100, 100],
                         random_state = 0).fit(X_train, y_train)
    
    title = 'Dataset 2: NN classifier, alpha = {:.3f} '.format(this_alpha)
    
    plot_class_regions_for_classifier_subplot(nnclf, X_train, y_train,
                                             X_test, y_test, title, axis)
    plt.tight_layout()

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

/Users/victormorales/opt/anaconda3/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:546: 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)

13.4. Aplicación

from sklearn.datasets import load_breast_cancer
# Breast cancer dataset para clasificación
cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)

from sklearn.neural_network import MLPClassifier
from sklearn.preprocessing import MinMaxScaler


scaler = MinMaxScaler()

X_train, X_test, y_train, y_test = train_test_split(X_cancer, y_cancer, random_state = 0)
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

clf = MLPClassifier(hidden_layer_sizes = [100, 100], alpha = 5.0,
                   random_state = 0, solver='lbfgs').fit(X_train_scaled, y_train)

print('Datos de cáncer de mama')
print('Precisión de NN en los datos de entrenamiento: {:.2f}'
     .format(clf.score(X_train_scaled, y_train)))
print('Precisión de NN en los datos de prueba: {:.2f}'
     .format(clf.score(X_test_scaled, y_test)))

Datos de cáncer de mama
Precisión de NN en los datos de entrenamiento: 0.98
Precisión de NN en los datos de prueba: 0.97