本篇接第九篇:《机器学习之神经网络(实战篇)》
这是一个比较完整的实战项目
import numpy as np import matplotlib.pyplot as plt %matplotlib inline # 放置数据的点 np.random.seed(0) N = 100 # 每类点数 D = 2 # 维度 K = 3 # 类别数目 X = np.zeros((N*K,D)) y = np.zeros(N*K, dtype='uint8') for j in range(K): ix = range(N*j,N*(j+1)) r = np.linspace(0.0,1,N) # 半径 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 fig = plt.figure(figsize=(11,11)) plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral) plt.show()
h = 200 # 隐藏层大小 W = 0.01 * np.random.randn(D,h)# x:300*2 2*100 b = np.zeros((1,h)) W2 = 0.01 * np.random.randn(h,K) b2 = np.zeros((1,K)) # 一些超参数 step_size = 1e-0 reg = 1e-3 # 正则化强度 # 梯度下降环 num_examples = X.shape[0] # 进行迭代训练模型 for i in range(10000): # 评价班级成绩, [N x K] hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation hidden_layer:300*100 #print hidden_layer.shape scores = np.dot(hidden_layer, W2) + b2 #scores:300*3 #print scores.shape # 计算类概率 exp_scores = np.exp(scores) probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K] #print probs.shape # 计算损耗:平均交叉熵损失与正则化 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 ("训练第 %d 次: 误差 %f" % (i, loss)) # 计算分数的梯度 dscores = probs dscores[range(num_examples),y] -= 1 dscores /= num_examples # 反向传播 参数的梯度 # 首先 反向传播 into parameters W2 and b2 dW2 = np.dot(hidden_layer.T, dscores) db2 = np.sum(dscores, axis=0, keepdims=True) # 然后 反向传播 into hidden layer dhidden = np.dot(dscores, W2.T) # 反向传播 the ReLU non-linearity dhidden[hidden_layer <= 0] = 0 # 最后 into W,b dW = np.dot(X.T, dhidden) db = np.sum(dhidden, axis=0, keepdims=True) # 添加正则化梯度贡献 dW2 += reg * W2 dW += reg * W # 执行参数更新 W += -step_size * dW b += -step_size * db W2 += -step_size * dW2 b2 += -step_size * db2 hidden_layer = np.maximum(0, np.dot(X, W) + b) scores = np.dot(hidden_layer, W2) + b2 predicted_class = np.argmax(scores, axis=1) print ('训练后的准确度: %.2f' % (np.mean(predicted_class == y))) h = 0.02 x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1 y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx, 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) + b2 Z = np.argmax(Z, axis=1) Z = Z.reshape(xx.shape) fig = plt.figure(figsize=(9,9)) plt.xticks(fontsize=20) plt.yticks(fontsize=20) 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()
训练的情况
最后的效果图