Python基于numpy灵活定义神经网络结构的方法

'''示例一'''
nn = NeuralNetworks([3,4,2]) # 定义神经网络
nn.fit(X,y) # 拟合
print(nn.predict(X)) #预测

'''示例二'''
nn = NeuralNetworks([3,5,7,4,2]) # 定义神经网络
nn.fit(X,y) # 拟合
print(nn.predict(X)) #预测

import numpy as np
class NeuralNetworks(object):
  ''''''
  def __init__(self, n_layers=None, active_type=None, n_iter=10000, error=0.05, alpha=0.5, lamda=0.4):
    '''搭建神经网络框架'''
    # 各层节点数目 (向量)
    self.n = np.array(n_layers) # 'n_layers必须为list类型，如：[3,4,2] 或 n_layers=[3,4,2]'
    self.size = self.n.size # 层的总数
    # 层 (向量)
    self.z = np.empty(self.size, dtype=object) # 先占位(置空)，dtype=object ！如下皆然
    self.a = np.empty(self.size, dtype=object)
    self.data_a = np.empty(self.size, dtype=object)
    # 偏置 (向量)
    self.b = np.empty(self.size, dtype=object)
    self.delta_b = np.empty(self.size, dtype=object)
    # 权 (矩阵)
    self.w = np.empty(self.size, dtype=object)
    self.delta_w = np.empty(self.size, dtype=object)
    # 填充
    for i in range(self.size):
      self.a[i] = np.zeros(self.n[i]) # 全零
      self.z[i] = np.zeros(self.n[i]) # 全零
      self.data_a[i] = np.zeros(self.n[i]) # 全零
      if i < self.size - 1:
        self.b[i] = np.ones(self.n[i+1])  # 全一
        self.delta_b[i] = np.zeros(self.n[i+1]) # 全零
        mu, sigma = 0, 0.1 # 均值、方差
        self.w[i] = np.random.normal(mu, sigma, (self.n[i], self.n[i+1])) # # 正态分布随机化
        self.delta_w[i] = np.zeros((self.n[i], self.n[i+1])) # 全零

import numpy as np
'''
参考：http://ufldl.stanford.edu/wiki/index.php/%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C
'''
class NeuralNetworks(object):
  ''''''
  def __init__(self, n_layers=None, active_type=None, n_iter=10000, error=0.05, alpha=0.5, lamda=0.4):
    '''搭建神经网络框架'''
    self.n_iter = n_iter # 迭代次数
    self.error = error # 允许最大误差
    self.alpha = alpha # 学习速率
    self.lamda = lamda # 衰减因子 # 此处故意拼写错误！
    if n_layers is None:
      raise '各层的节点数目必须设置！'
    elif not isinstance(n_layers, list):
      raise 'n_layers必须为list类型，如：[3,4,2] 或 n_layers=[3,4,2]'
    # 节点数目 (向量)
    self.n = np.array(n_layers)
    self.size = self.n.size # 层的总数
    # 层 (向量)
    self.a = np.empty(self.size, dtype=object) # 先占位(置空)，dtype=object ！如下皆然
    self.z = np.empty(self.size, dtype=object)
    # 偏置 (向量)
    self.b = np.empty(self.size, dtype=object)
    self.delta_b = np.empty(self.size, dtype=object)
    # 权 (矩阵)
    self.w = np.empty(self.size, dtype=object)
    self.delta_w = np.empty(self.size, dtype=object)
    # 残差 (向量)
    self.data_a = np.empty(self.size, dtype=object)
    # 填充
    for i in range(self.size):
      self.a[i] = np.zeros(self.n[i]) # 全零
      self.z[i] = np.zeros(self.n[i]) # 全零
      self.data_a[i] = np.zeros(self.n[i]) # 全零
      if i < self.size - 1:
        self.b[i] = np.ones(self.n[i+1])  # 全一
        self.delta_b[i] = np.zeros(self.n[i+1]) # 全零
        mu, sigma = 0, 0.1 # 均值、方差
        self.w[i] = np.random.normal(mu, sigma, (self.n[i], self.n[i+1])) # # 正态分布随机化
        self.delta_w[i] = np.zeros((self.n[i], self.n[i+1])) # 全零
    # 激活函数
    self.active_functions = {
      'sigmoid': self.sigmoid,
      'tanh': self.tanh,
      'radb': self.radb,
      'line': self.line,
    }
    # 激活函数的导函数
    self.derivative_functions = {
      'sigmoid': self.sigmoid_d,
      'tanh': self.tanh_d,
      'radb': self.radb_d,
      'line': self.line_d,
    }
    if active_type is None:
      self.active_type = ['sigmoid'] * (self.size - 1) # 默认激活函数类型
    else:
      self.active_type = active_type
  def sigmoid(self, z):
    if np.max(z) > 600:
      z[z.argmax()] = 600
    return 1.0 / (1.0 + np.exp(-z))
  def tanh(self, z):
    return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))
  def radb(self, z):
    return np.exp(-z * z)
  def line(self, z):
    return z
  def sigmoid_d(self, z):
    return z * (1.0 - z)
  def tanh_d(self, z):
    return 1.0 - z * z
  def radb_d(self, z):
    return -2.0 * z * np.exp(-z * z)
  def line_d(self, z):
    return np.ones(z.size) # 全一
  def forward(self, x):
    '''正向传播（在线）''' 
    # 用样本 x 走一遍，刷新所有 z, a
    self.a[0] = x
    for i in range(self.size - 1):
      self.z[i+1] = np.dot(self.a[i], self.w[i]) + self.b[i] 
      self.a[i+1] = self.active_functions[self.active_type[i]](self.z[i+1]) # 加了激活函数
  def err(self, X, Y):
    '''误差'''
    last = self.size-1
    err = 0.0
    for x, y in zip(X, Y):
      self.forward(x)
      err += 0.5 * np.sum((self.a[last] - y)**2)
    err /= X.shape[0]
    err += sum([np.sum(w) for w in self.w[:last]**2])
    return err
  def backward(self, y):
    '''反向传播（在线）'''
    last = self.size - 1
    # 用样本 y 走一遍，刷新所有delta_w, delta_b
    self.data_a[last] = -(y - self.a[last]) * self.derivative_functions[self.active_type[last-1]](self.z[last]) # 加了激活函数的导函数
    for i in range(last-1, 1, -1):
      self.data_a[i] = np.dot(self.w[i], self.data_a[i+1]) * self.derivative_functions[self.active_type[i-1]](self.z[i]) # 加了激活函数的导函数
      # 计算偏导
      p_w = np.outer(self.a[i], self.data_a[i+1]) # 外积！感谢 numpy 的强大！
      p_b = self.data_a[i+1]
      # 更新 delta_w, delta_w
      self.delta_w[i] = self.delta_w[i] + p_w
      self.delta_b[i] = self.delta_b[i] + p_b
  def update(self, n_samples):
    '''更新权重参数'''
    last = self.size - 1
    for i in range(last):
      self.w[i] -= self.alpha * ((1/n_samples) * self.delta_w[i] + self.lamda * self.w[i])
      self.b[i] -= self.alpha * ((1/n_samples) * self.delta_b[i])
  def fit(self, X, Y):
    '''拟合'''
    for i in range(self.n_iter):
      # 用所有样本，依次
      for x, y in zip(X, Y):
        self.forward(x) # 前向，更新 a, z;
        self.backward(y) # 后向，更新 delta_w, delta_b
      # 然后，更新 w, b
      self.update(len(X))
      # 计算误差
      err = self.err(X, Y)
      if err < self.error:
        break
      # 整千次显示误差（否则太无聊！）
      if i % 1000 == 0:
        print('iter: {}, error: {}'.format(i, err))
  def predict(self, X):
    '''预测'''
    last = self.size - 1
    res = []
    for x in X:
      self.forward(x)
      res.append(self.a[last])
    return np.array(res)
if __name__ == '__main__':
  nn = NeuralNetworks([2,3,4,3,1], n_iter=5000, alpha=0.4, lamda=0.3, error=0.06) # 定义神经网络
  X = np.array([[0.,0.], # 准备数据
         [0.,1.],
         [1.,0.],
         [1.,1.]])
  y = np.array([0,1,1,0])
  nn.fit(X,y)     # 拟合
  print(nn.predict(X)) # 预测