BP神經(jīng)網(wǎng)絡(luò)是最簡(jiǎn)單的神經(jīng)網(wǎng)絡(luò)模型了，三層能夠模擬非線性函數(shù)效果。

難點(diǎn)：

如何確定初始化參數(shù)？

如何確定隱含層節(jié)點(diǎn)數(shù)量？

迭代多少次？如何更快收斂？

如何獲得全局最優(yōu)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();

具體收斂效果

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