基于python的BP神经网络及异或实现过程解析

Python  /  管理员 发布于 7年前   169

BP神经网络是最简单的神经网络模型了，三层能够模拟非线性函数效果。

难点：

• 如何确定初始化参数？
• 如何确定隐含层节点数量？
• 迭代多少次？如何更快收敛？
• 如何获得全局最优解？

'''neural networks created on 2019.9.24author: vince'''import mathimport loggingimport numpy import randomimport matplotlib.pyplot as plt'''neural network '''class NeuralNetwork: def __init__(self, layer_nums, iter_num = 10000, batch_size = 1):  self.__ILI = 0;  self.__HLI = 1;  self.__OLI = 2;  self.__TLN = 3;  if len(layer_nums) != self.__TLN:   raise Exception("layer_nums length must be 3");  self.__layer_nums = layer_nums; #array [layer0_num, layer1_num ...layerN_num]  self.__iter_num = iter_num;  self.__batch_size = batch_size;  def train(self, X, Y):  X = numpy.array(X);  Y = numpy.array(Y);  self.L = [];  #initialize parameters  self.__weight = [];  self.__bias = [];  self.__step_len = [];  for layer_index in range(1, self.__TLN):   self.__weight.append(numpy.random.rand(self.__layer_nums[layer_index - 1], self.__layer_nums[layer_index]) * 2 - 1.0);   self.__bias.append(numpy.random.rand(self.__layer_nums[layer_index]) * 2 - 1.0);   self.__step_len.append(0.3);  logging.info("bias:%s" % (self.__bias));  logging.info("weight:%s" % (self.__weight));  for iter_index in range(self.__iter_num):   sample_index = random.randint(0, len(X) - 1);   logging.debug("-----round:%s, select sample %s-----" % (iter_index, sample_index));   output = self.forward_pass(X[sample_index]);   g = (-output[2] + Y[sample_index]) * self.activation_drive(output[2]);   logging.debug("g:%s" % (g));   for j in range(len(output[1])):    self.__weight[1][j] += self.__step_len[1] * g * output[1][j];   self.__bias[1] -= self.__step_len[1] * g;   e = [];   for i in range(self.__layer_nums[self.__HLI]):    e.append(numpy.dot(g, self.__weight[1][i]) * self.activation_drive(output[1][i]));   e = numpy.array(e);   logging.debug("e:%s" % (e));   for j in range(len(output[0])):    self.__weight[0][j] += self.__step_len[0] * e * output[0][j];   self.__bias[0] -= self.__step_len[0] * e;   l = 0;   for i in range(len(X)):    predictions = self.forward_pass(X[i])[2];    l += 0.5 * numpy.sum((predictions - Y[i]) ** 2);   l /= len(X);   self.L.append(l);   logging.debug("bias:%s" % (self.__bias));   logging.debug("weight:%s" % (self.__weight));   logging.debug("loss:%s" % (l));  logging.info("bias:%s" % (self.__bias));  logging.info("weight:%s" % (self.__weight));  logging.info("L:%s" % (self.L));  def activation(self, z):  return (1.0 / (1.0 + numpy.exp(-z))); def activation_drive(self, y):  return y * (1.0 - y); def forward_pass(self, x):  data = numpy.copy(x);  result = [];  result.append(data);  for layer_index in range(self.__TLN - 1):   data = self.activation(numpy.dot(data, self.__weight[layer_index]) - self.__bias[layer_index]);   result.append(data);  return numpy.array(result); def predict(self, x):  return self.forward_pass(x)[self.__OLI];def main(): logging.basicConfig(level = logging.INFO,   format = '%(asctime)s %(filename)s[line:%(lineno)d] %(levelname)s %(message)s',   datefmt = '%a, %d %b %Y %H:%M:%S');    logging.info("trainning begin."); nn = NeuralNetwork([2, 2, 1]); X = numpy.array([[0, 0], [1, 0], [1, 1], [0, 1]]); Y = numpy.array([0, 1, 0, 1]); nn.train(X, Y); logging.info("trainning end. predict begin."); for x in X:  print(x, nn.predict(x)); plt.plot(nn.L) plt.show();if __name__ == "__main__": main();

具体收敛效果

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