Python实现的NN神经网络算法完整示例

# -*- coding:utf-8 -*-#!python3__author__ = 'Wsine'import numpy as npimport sklearnimport sklearn.datasetsimport sklearn.linear_modelimport matplotlib.pyplot as pltimport matplotlibimport operatorimport timedef createData(dim=200, cnoise=0.20):  """  输出：数据集, 对应的类别标签  描述：生成一个数据集和对应的类别标签  """  np.random.seed(0)  X, y = sklearn.datasets.make_moons(dim, noise=cnoise)  plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)  #plt.show()  return X, ydef plot_decision_boundary(pred_func, X, y):  """  输入：边界函数, 数据集, 类别标签  描述：绘制决策边界(画图用)  """  # 设置最小最大值, 加上一点外边界  x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5  y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5  h = 0.01  # 根据最小最大值和一个网格距离生成整个网格  xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))  # 对整个网格预测边界值  Z = pred_func(np.c_[xx.ravel(), yy.ravel()])  Z = Z.reshape(xx.shape)  # 绘制边界和数据集的点  plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)  plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)def calculate_loss(model, X, y):  """  输入：训练模型, 数据集, 类别标签  输出：误判的概率  描述：计算整个模型的性能  """  W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']  # 正向传播来计算预测的分类值  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)  # 计算误判概率  corect_logprobs = -np.log(probs[range(num_examples), y])  data_loss = np.sum(corect_logprobs)  # 加入正则项修正错误(可选)  data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))  return 1./num_examples * data_lossdef predict(model, x):  """  输入：训练模型, 预测向量  输出：判决类别  描述：预测类别属于(0 or 1)  """  W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']  # 正向传播计算  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)def initParameter(X):  """  输入：数据集  描述：初始化神经网络算法的参数     必须初始化为全局函数！     这里需要手动设置！  """  global num_examples  num_examples = len(X) # 训练集的大小  global nn_input_dim  nn_input_dim = 2 # 输入层维数  global nn_output_dim  nn_output_dim = 2 # 输出层维数  # 梯度下降参数  global epsilon  epsilon = 0.01 # 梯度下降学习步长  global reg_lambda  reg_lambda = 0.01 # 修正的指数def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False):  """  输入：数据集, 类别标签, 隐藏层层数, 迭代次数, 是否输出误判率  输出：神经网络模型  描述：生成一个指定层数的神经网络模型  """  # 根据维度随机初始化参数  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))  model = {}  # 梯度下降  for i in range(0, num_passes):    # 正向传播    z1 = X.dot(W1) + b1    a1 = np.tanh(z1) # 激活函数使用tanh = (exp(x) - exp(-x)) / (exp(x) + exp(-x))    z2 = a1.dot(W2) + b2    exp_scores = np.exp(z2) # 原始归一化    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)    # 后向传播    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)    # 加入修正项    dW2 += reg_lambda * W2    dW1 += reg_lambda * W1    # 更新梯度下降参数    W1 += -epsilon * dW1    b1 += -epsilon * db1    W2 += -epsilon * dW2    b2 += -epsilon * db2    # 更新模型    model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}    # 一定迭代次数后输出当前误判率    if print_loss and i % 1000 == 0:      print("Loss after iteration %i: %f" % (i, calculate_loss(model, X, y)))  plot_decision_boundary(lambda x: predict(model, x), X, y)  plt.title("Decision Boundary for hidden layer size %d" % nn_hdim)  #plt.show()  return modeldef main():  dataSet, labels = createData(200, 0.20)  initParameter(dataSet)  nnModel = build_model(dataSet, labels, 3, print_loss=False)  print("Loss is %f" % calculate_loss(nnModel, dataSet, labels))if __name__ == '__main__':  start = time.clock()  main()  end = time.clock()  print('finish all in %s' % str(end - start))  plt.show()