from __future__ import print_function, division import numpy as np import math from sklearn import datasets from mlfromscratch.utils import train_test_split, to_categorical, normalize, accuracy_score, Plot from mlfromscratch.deep_learning.activation_functions import Sigmoid, Softmax from mlfromscratch.deep_learning.loss_functions import CrossEntropy class MultilayerPerceptron(): """Multilayer Perceptron classifier. A fully-connected neural network with one hidden layer. Unrolled to display the whole forward and backward pass. Parameters: ----------- n_hidden: int: The number of processing nodes (neurons) in the hidden layer. n_iterations: float The number of training iterations the algorithm will tune the weights for. learning_rate: float The step length that will be used when updating the weights. """ def __init__(self, n_hidden, n_iterations=3000, learning_rate=0.01): self.n_hidden = n_hidden self.n_iterations = n_iterations self.learning_rate = learning_rate self.hidden_activation = Sigmoid() self.output_activation = Softmax() self.loss = CrossEntropy() def _initialize_weights(self, X, y): n_samples, n_features = X.shape _, n_outputs = y.shape # Hidden layer limit = 1 / math.sqrt(n_features) self.W = np.random.uniform(-limit, limit, (n_features, self.n_hidden)) self.w0 = np.zeros((1, self.n_hidden)) # Output layer limit = 1 / math.sqrt(self.n_hidden) self.V = np.random.uniform(-limit, limit, (self.n_hidden, n_outputs)) self.v0 = np.zeros((1, n_outputs)) def fit(self, X, y): self._initialize_weights(X, y) for i in range(self.n_iterations): # .............. # Forward Pass # .............. # HIDDEN LAYER hidden_input = X.dot(self.W) + self.w0 hidden_output = self.hidden_activation(hidden_input) # OUTPUT LAYER output_layer_input = hidden_output.dot(self.V) + self.v0 y_pred = self.output_activation(output_layer_input) # ............... # Backward Pass # ............... # OUTPUT LAYER # Grad. w.r.t input of output layer grad_wrt_out_l_input = self.loss.gradient(y, y_pred) * self.output_activation.gradient(output_layer_input) grad_v = hidden_output.T.dot(grad_wrt_out_l_input) grad_v0 = np.sum(grad_wrt_out_l_input, axis=0, keepdims=True) # HIDDEN LAYER # Grad. w.r.t input of hidden layer grad_wrt_hidden_l_input = grad_wrt_out_l_input.dot(self.V.T) * self.hidden_activation.gradient(hidden_input) grad_w = X.T.dot(grad_wrt_hidden_l_input) grad_w0 = np.sum(grad_wrt_hidden_l_input, axis=0, keepdims=True) # Update weights (by gradient descent) # Move against the gradient to minimize loss self.V -= self.learning_rate * grad_v self.v0 -= self.learning_rate * grad_v0 self.W -= self.learning_rate * grad_w self.w0 -= self.learning_rate * grad_w0 # Use the trained model to predict labels of X def predict(self, X): # Forward pass: hidden_input = X.dot(self.W) + self.w0 hidden_output = self.hidden_activation(hidden_input) output_layer_input = hidden_output.dot(self.V) + self.v0 y_pred = self.output_activation(output_layer_input) return y_pred def main(): data = datasets.load_digits() X = normalize(data.data) y = data.target # Convert the nominal y values to binary y = to_categorical(y) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, seed=1) # MLP clf = MultilayerPerceptron(n_hidden=16, n_iterations=1000, learning_rate=0.01) clf.fit(X_train, y_train) y_pred = np.argmax(clf.predict(X_test), axis=1) y_test = np.argmax(y_test, axis=1) accuracy = accuracy_score(y_test, y_pred) print ("Accuracy:", accuracy) # Reduce dimension to two using PCA and plot the results Plot().plot_in_2d(X_test, y_pred, title="Multilayer Perceptron", accuracy=accuracy, legend_labels=np.unique(y)) if __name__ == "__main__": main()