用python实现BP神经网络

#coding=utf-8import numpy as npimport sklearn.datasetsimport sklearn.linear_modelimport matplotlib.pyplot as pltfrom mlxtend.evaluate import plot_decision_regionsimport sys# Generate a dataset and plot itnp.random.seed(0)X, y = sklearn.datasets.make_moons(200, noise=0.20)plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)#plt.show()# # Train the logistic rgeression classifier# clf = sklearn.linear_model.LogisticRegressionCV()# clf.fit(X, y)# # Plot the decision boundary# plot_decision_regions(X,y,clf.fit(X,y),legend=0) #legend=0表示没有图例，看函数说明# plt.title("Logistic Regression")# #plt.show()#－－－－－－－－－－－－－－－－－－－－－－－－－－－#BP#定义梯度下降一些有用的变量和参数num_examples = len(X) # training set sizenn_input_dim = 2 # input layer dimensionalitynn_output_dim = 2 # output layer dimensionality# Gradient descent parameters (I picked these by hand)epsilon = 0.01 # learning rate for gradient descentreg_lambda = 0.01 # regularization strengthclass tempmodel():    model={}    # Helper function to evaluate the total loss on the dataset    def calculate_loss(self):        W1, b1, W2, b2 = self.model['W1'], self.model['b1'], self.model['W2'], self.model['b2']        # Forward propagation to calculate our predictions        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)        # Calculating the loss        corect_logprobs = -np.log(probs[range(num_examples), y])        data_loss = np.sum(corect_logprobs)        # Add regulatization term to loss (optional)        data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))        return 1./num_examples * data_loss    # Helper function to predict an output (0 or 1)    def predict(self, X): #这个‘X’大小写都无所谓，因为，predict是函数plot_decision_regions自己调用的，会自动以第一个函数传入给‘X’        W1, b1, W2, b2 = self.model['W1'], self.model['b1'], self.model['W2'], self.model['b2']        # 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)        return np.argmax(probs, axis=1)    # This function learns parameters for the neural network and returns the model.    # - nn_hdim: Number of nodes in the hidden layer    # - num_passes: Number of passes through the training data for gradient descent    # - print_loss: If True, print the loss every 1000 iterations    def build_model(self,nn_hdim, num_passes=20000, print_loss=False):        # Initialize the parameters to random values. We need to learn these.        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))        # This is what we return at the end        model = {}        # Gradient descent. For each batch...        for i in xrange(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 += -epsilon * dW1            b1 += -epsilon * db1            W2 += -epsilon * dW2            b2 += -epsilon * db2            # Assign new parameters to the model            self.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 "Loss after iteration %i: %f" %(i, self.calculate_loss())if __name__=='__main__':try:if len(sys.argv)<2:degree=3else:degree=int(sys.argv[1])except:print "usage:python 2BP.py degree(a number,default equal to 3)"sys.exit(0)rmodel=tempmodel()# Build a model with a 3-dimensional hidden layerrmodel.build_model(degree,print_loss=True)# Plot the decision boundaryplot_decision_regions(X,y,rmodel,legend=0) #必须改成类模式，因为这个函数要求传入的对象有predict函数plt.title("Decision Boundary for hidden layer size %d"%degree)plt.show()

原网址：http://python.jobbole.com/82208/，讲的非常好，但是那里的代码已经不能用了，感谢原作者

这里的代码能在python2.7，mlxtend-0.3.0下运行。

效果图如下：