cs231n一次课程实践，python实现softmax线性分类器和二层神经网络

看了以后，对bp算法的实现有直观的认识，真的太棒了！

import numpy as npimport matplotlib.pyplot as pltnp.random.seed(0)N = 100 # 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# lets visualize the data:#plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)#plt.show()# initialize parameters randomlyh = 100  # 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))# some hyperparametersstep_size = 1e-0reg = 1e-3  # regularization strength# gradient descent loopnum_examples = X.shape[0]for i in xrange(10000):    # evaluate class scores, [N x K]    hidden_layer = np.maximum(0, np.dot(X, W) + b)  # note, ReLU activation    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))# plot the resulting classifierh = 0.02x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1xx, yy = np.meshgrid(np.arange(x_min, x_max, h),                     np.arange(y_min, y_max, h))Z = np.dot(np.maximum(0, np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b), W2) + b2Z = np.argmax(Z, axis=1)Z = Z.reshape(xx.shape)fig = plt.figure()plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)plt.xlim(xx.min(), xx.max())plt.ylim(yy.min(), yy.max())plt.show()#fig.savefig('spiral_net.png')

线性分类器，loss为softmax loss，注意softmax的梯度形式

import numpy as npimport matplotlib.pyplot as pltnp.random.seed(0)N = 100 # 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# lets visualize the data:#plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)#plt.show()# Train a Linear Classifier# initialize parameters randomlyW = 0.01 * np.random.randn(D, K)b = np.zeros((1, K))# some hyperparametersstep_size = 1e-0reg = 1e-3  # regularization strength# gradient descent loopnum_examples = X.shape[0]for i in xrange(200):  # evaluate class scores, [N x K]  scores = np.dot(X, W) + b  # 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)  loss = data_loss + reg_loss  if i % 10 == 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 (W,b)  dW = np.dot(X.T, dscores)  db = np.sum(dscores, axis=0, keepdims=True)  dW += reg * W  # regularization gradient  # perform a parameter update  W += -step_size * dW  b += -step_size * db# evaluate training set accuracyscores = np.dot(X, W) + bpredicted_class = np.argmax(scores, axis=1)print 'training accuracy: %.2f' % (np.mean(predicted_class == y))# plot the resulting classifierh = 0.02x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1xx, yy = np.meshgrid(np.arange(x_min, x_max, h),                     np.arange(y_min, y_max, h))Z = np.dot(np.c_[xx.ravel(), yy.ravel()], W) + bZ = np.argmax(Z, axis=1)Z = Z.reshape(xx.shape)#fig = plt.figure()plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)plt.xlim(xx.min(), xx.max())plt.ylim(yy.min(), yy.max())#plt.show()#fig.savefig('spiral_linear.png')