# # BP demo code # # reference: # https://www.2cto.com/kf/201612/543750.html # import numpy as np from sklearn import datasets, linear_model import matplotlib.pyplot as plt class Config: nn_input_dim = 2 nn_output_dim = 2 epsilon = 0.01 reg_lambda = 0.01 def generate_data(): np.random.seed(0) X, y = datasets.make_moons(200, noise=0.20) return X, y def visualize(X, y, model): plot_decision_boundary(lambda x:predict(model,x), X, y) plt.title("Logistic Regression") def plot_decision_boundary(pred_func, X, y): x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5 y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5 h = 0.01 xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) Z = pred_func(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral) plt.show() def predict(model, x): W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2'] z1 = x.dot(W1) + b1 a1 = np.tanh(z1) z2 = a1.dot(W2) + b2 exp_scores = np.exp(z2) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) return np.argmax(probs, axis=1) def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False): num_examples = len(X) np.random.seed(0) W1 = np.random.randn(Config.nn_input_dim, nn_hdim) / np.sqrt(Config.nn_input_dim) b1 = np.zeros((1, nn_hdim)) W2 = np.random.randn(nn_hdim, Config.nn_output_dim) / np.sqrt(nn_hdim) b2 = np.zeros((1, Config.nn_output_dim)) model = {} for i in range(0, num_passes): z1 = X.dot(W1) + b1 a1 = np.tanh(z1) z2 = a1.dot(W2) + b2 exp_scores = np.exp(z2) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) delta3 = probs delta3[range(num_examples), y] -= 1 dW2 = (a1.T).dot(delta3) db2 = np.sum(delta3, axis=0, keepdims=True) delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2)) dW1 = np.dot(X.T, delta2) db1 = np.sum(delta2, axis=0) dW2 += Config.reg_lambda * W2 dW1 += Config.reg_lambda * W1 W1 += -Config.epsilon * dW1 b1 += -Config.epsilon * db1 W2 += -Config.epsilon * dW2 b2 += -Config.epsilon * db2 model = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2} return model def main(): X, y = generate_data() model = build_model(X, y, 3) visualize(X, y, model) if __name__ == "__main__": main()