import numpy as np import matplotlib.pyplot as plt np.random.seed(100) class Layer: """ Represents a layer (hidden or output) in our neural network. """ def __init__(self, n_input, n_neurons, activation=None, weights=None, bias=None): """ :param int n_input: The input size (coming from the input layer or a previous hidden layer) :param int n_neurons: The number of neurons in this layer. :param str activation: The activation function to use (if any). :param weights: The layer's weights. :param bias: The layer's bias. """ self.weights = weights if weights is not None else np.random.rand(n_input, n_neurons) self.activation = activation self.bias = bias if bias is not None else np.zeros(n_neurons) self.last_activation = None self.error = None self.delta = None def activate(self, x): """ Calculates the dot product of this layer. :param x: The input. :return: The result. """ r = np.dot(x, self.weights) + self.bias self.last_activation = self._apply_activation(r) return self.last_activation def _apply_activation(self, r): """ Applies the chosen activation function (if any). :param r: The normal value. :return: The "activated" value. """ # In case no activation function was chosen if self.activation is None: return r # tanh if self.activation == 'tanh': return np.tanh(r) # sigmoid if self.activation == 'sigmoid': return 1 / (1 + np.exp(-r)) return r def apply_activation_derivative(self, r): """ Applies the derivative of the activation function (if any). :param r: The normal value. :return: The "derived" value. """ # We use 'r' directly here because its already activated, the only values that # are used in this function are the last activations that were saved. if self.activation is None: return r if self.activation == 'tanh': return 1 - r ** 2 if self.activation == 'sigmoid': return r * (1 - r) return r class NeuralNetwork: """ Represents a neural network. """ def __init__(self): self._layers = [] def add_layer(self, layer): """ Adds a layer to the neural network. :param Layer layer: The layer to add. """ self._layers.append(layer) def feed_forward(self, X): """ Feed forward the input through the layers. :param X: The input values. :return: The result. """ for layer in self._layers: X = layer.activate(X) return X def predict(self, X): """ Predicts a class (or classes). :param X: The input values. :return: The predictions. """ ff = self.feed_forward(X) # One row if ff.ndim == 1: return np.argmax(ff) # Multiple rows return np.argmax(ff, axis=1) def backpropagation(self, X, y, learning_rate): """ Performs the backward propagation algorithm and updates the layers weights. :param X: The input values. :param y: The target values. :param float learning_rate: The learning rate (between 0 and 1). """ # Feed forward for the output output = self.feed_forward(X) # Loop over the layers backward for i in reversed(range(len(self._layers))): layer = self._layers[i] # If this is the output layer if layer == self._layers[-1]: layer.error = y - output # The output = layer.last_activation in this case layer.delta = layer.error * layer.apply_activation_derivative(output) else: next_layer = self._layers[i + 1] layer.error = np.dot(next_layer.weights, next_layer.delta) layer.delta = layer.error * layer.apply_activation_derivative(layer.last_activation) # Update the weights for i in range(len(self._layers)): layer = self._layers[i] # The input is either the previous layers output or X itself (for the first hidden layer) input_to_use = np.atleast_2d(X if i == 0 else self._layers[i - 1].last_activation) layer.weights += layer.delta * input_to_use.T * learning_rate def train(self, X, y, learning_rate, max_epochs): """ Trains the neural network using backpropagation. :param X: The input values. :param y: The target values. :param float learning_rate: The learning rate (between 0 and 1). :param int max_epochs: The maximum number of epochs (cycles). :return: The list of calculated MSE errors. """ mses = [] for i in range(max_epochs): for j in range(len(X)): self.backpropagation(X[j], y[j], learning_rate) if i % 10 == 0: mse = np.mean(np.square(y - nn.feed_forward(X))) mses.append(mse) print('Epoch: #%s, MSE: %f' % (i, float(mse))) return mses @staticmethod def accuracy(y_pred, y_true): """ Calculates the accuracy between the predicted labels and true labels. :param y_pred: The predicted labels. :param y_true: The true labels. :return: The calculated accuracy. """ return (y_pred == y_true).mean() nn = NeuralNetwork() nn.add_layer(Layer(2, 30, 'sigmoid')) nn.add_layer(Layer(30, 30, 'sigmoid')) nn.add_layer(Layer(30, 30, 'sigmoid')) nn.add_layer(Layer(30, 3, 'sigmoid')) nn.add_layer(Layer(3, 1, 'sigmoid')) # Define dataset X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]]) y = np.array([[0], [1], [1], [0]]) # Train the neural network errors = nn.train(X, y, 0.03, 290) print('Accuracy: %.2f%%' % (nn.accuracy(nn.predict(X), y.flatten()) * 100)) # Plot changes in mse plt.plot(errors) plt.title('Changes in MSE') plt.xlabel('Epoch (every 10th)') plt.ylabel('MSE') plt.show()