Python实现的NN神经网络算法完整示例

# -*- coding:utf-8 -*-
#!python3
__author__ = 'Wsine'
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
import matplotlib.pyplot as plt
import matplotlib
import operator
import time
def 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, y
def 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_loss
def 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 model
def 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()