用python实现一个神经网络

原文：http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/

体验一下神经网络

# -*- coding: utf-8 -*-"""Created on Fri Jul  7 15:37:41 2017@author: bryan"""import numpy as npfrom matplotlib import pyplot as pltimport sklearnnp.random.seed(0)X, y = sklearn.datasets.make_moons(200, noise=0.20)num_examples=len(X)nn_input_dim=2nn_output_dim=2#Gradient descent parameterseta=0.01reg_lambda=0.01def plot_decision_boundary(pred_func):    # Set min and max values and give it some padding    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    # Generate a grid of points with distance h between them    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))    # Predict the function value for the whole gid    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])    Z = Z.reshape(xx.shape)    # Plot the contour and training examples    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)def calculate_loss(model):    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)    corect_logprobs=-np.log(probs[range(num_examples),y])    data_loss = np.sum(corect_logprobs)    data_loss+=reg_lambda/2*(np.sum(np.square(W1))+np.sum(np.square(W2)))    return 1./num_examples*data_lossdef 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(nn_hdim,num_passes=20000,print_loss=True):    np.random.seed(0)    W1=np.random.randn(nn_input_dim,nn_hdim)/np.sqrt(nn_input_dim)    b1=np.zeros((1,nn_hdim))    W2=np.random.randn(nn_hdim,nn_output_dim)/np.sqrt(nn_hdim)    b2 = np.zeros((1, nn_output_dim))    model={}    # Gradient descent. For each batch...    for i in range(0,num_passes):        # Forward propagation        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)                # Backpropagation        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)                # Add regularization terms (b1 and b2 don't have regularization terms)        dW2+=reg_lambda*W2        dW1+=reg_lambda*W1                # Gradient descent parameter update        W1+=-eta*dW1        b1+=-eta*db1        W2+=-eta*dW2        b2+=-eta*db2                model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}                # Optionally print the loss.        # This is expensive because it uses the whole dataset, so we don't want to do it too often.        if print_loss and i % 1000 == 0:            print( "%i hidden_layers' Loss after iteration %i: %f" %(nn_hdim,i, calculate_loss(model)))    return model # Build a model with a 3-dimensional hidden layer#model = build_model(3, print_loss=True) # Plot the decision boundary#plot_decision_boundary(lambda x: predict(model, x))#plt.title("Decision Boundary for hidden layer size 3")plt.figure(figsize=(16, 32))hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]for i, nn_hdim in enumerate(hidden_layer_dimensions):    plt.subplot(5, 2, i+1)    plt.title('Hidden Layer size %d' % nn_hdim)    model = build_model(nn_hdim)    plot_decision_boundary(lambda x: predict(model, x))plt.show()