Python: Neural Networks

这是用Python实现的Neural Networks, 基于Python 2.7.9, numpy, matplotlib。
代码来源于斯坦福大学的课程： http://cs231n.github.io/neural-networks-case-study/
基本是照搬过来，通过这个程序有助于了解python语法，以及Neural Networks 的原理。

import numpy as npimport matplotlib.pyplot as pltN = 200 # number of points per classD = 2 # dimensionalityK = 3 # number of classesX = np.zeros((N*K,D)) # data matrix (each row = single example)y = np.zeros(N*K, dtype='uint8') # class labelsfor j in xrange(K):  ix = range(N*j,N*(j+1))  r = np.linspace(0.0,1,N) # radius  t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta  X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]  y[ix] = j# print y# lets visualize the data:plt.scatter(X[:,0], X[:,1], s=40, c=y, alpha=0.5)plt.show()# Train a Linear Classifier# initialize parameters randomlyh = 20 # size of hidden layerW = 0.01 * np.random.randn(D,h)b = np.zeros((1,h))W2 = 0.01 * np.random.randn(h,K)b2 = np.zeros((1,K))# define some hyperparametersstep_size = 1e-0reg = 1e-3 # regularization strength# gradient descent loopnum_examples = X.shape[0]for i in xrange(1):  # evaluate class scores, [N x K]  hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation  # print np.size(hidden_layer,1)  scores = np.dot(hidden_layer, W2) + b2  # compute the class probabilities  exp_scores = np.exp(scores)  probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]  # compute the loss: average cross-entropy loss and regularization  corect_logprobs = -np.log(probs[range(num_examples),y])  data_loss = np.sum(corect_logprobs)/num_examples  reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)  loss = data_loss + reg_loss  if i % 1000 == 0:    print "iteration %d: loss %f" % (i, loss)  # compute the gradient on scores  dscores = probs  dscores[range(num_examples),y] -= 1  dscores /= num_examples  # backpropate the gradient to the parameters  # first backprop into parameters W2 and b2  dW2 = np.dot(hidden_layer.T, dscores)  db2 = np.sum(dscores, axis=0, keepdims=True)  # next backprop into hidden layer  dhidden = np.dot(dscores, W2.T)  # backprop the ReLU non-linearity  dhidden[hidden_layer <= 0] = 0  # finally into W,b  dW = np.dot(X.T, dhidden)  db = np.sum(dhidden, axis=0, keepdims=True)  # add regularization gradient contribution  dW2 += reg * W2  dW += reg * W  # perform a parameter update  W += -step_size * dW  b += -step_size * db  W2 += -step_size * dW2  b2 += -step_size * db2  # evaluate training set accuracyhidden_layer = np.maximum(0, np.dot(X, W) + b)scores = np.dot(hidden_layer, W2) + b2predicted_class = np.argmax(scores, axis=1)print 'training accuracy: %.2f' % (np.mean(predicted_class == y))

随机生成的数据

运行结果