【Python 代码】CS231n中Softmax线性分类器、非线性分类器对比举例（含python绘图显示结果）

#CS231n中线性、非线性分类器举例（Softmax）#注意其中反向传播的计算# -*- coding: utf-8 -*-import numpy as npimport matplotlib.pyplot as pltN = 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.xlim([-1, 1])plt.ylim([-1, 1])plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)plt.show()# initialize parameters randomly# 线性分类器W = 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())## initialize parameters randomly#  含一个隐层的非线性分类器 使用ReLUh = 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())