BP神经网络及异或实现

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：

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

 '''
 neural networks 

 created on 2019.9.24
 author: vince
 '''
 import math
 import logging
 import numpy
 import random
 import 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