这是机器学习笔记的第二篇，之前写了一篇：机器学习笔记-Python实现感知机(Perceptron) 。这篇博客在上篇博客代码的基础上实现了含单隐层的前馈神经网络，并实现了BP误差逆传播算法。
关于算法的内容，不多叙述，不如看书。
直接上代码：
# coding:utf-8
import math
def sigmoid(x):
return 1.0/(1+math.exp(-x))
class Record:
def __init__(self):
feature_vector = []
label = []
return
class Node:
def __init__(self):
self.input_list = []
self.activated = False
self.recent_output = None
self.threshold = 0.0
self.activation_func = lambda s: 1.0 / (1 + math.exp(-s)) # default func: sigmoid function
return
def add_input(self, node):
self.input_list.append([node, 1.0])
return
def set_threshold(self, th):
self.threshold = th
return
def output_(self):
if self.activated is True:
return self.recent_output
sum_ = 0.0
for p in self.input_list:
prev_node = p[0]
sum_ += prev_node.output_() * p[1]
self.recent_output = self.activation_func(sum_ - self.threshold)
self.activated = True
return self.recent_output
class InputNode(Node):
def __init__(self):
Node.__init__(self)
self.activation_func = lambda s: s
return
def set_input_val(self, val):
Node.set_threshold(self, -val)
return
class OutputNode(Node):
def __init__(self):
Node.__init__(self)
self.threshold = 4.0
return
class NeuralNetwork:
def __init__(self):
self.eta = 0.1
self.data_set = []
def set_data_set(self, data_set_):
self.data_set = data_set_
return
class SingleHiddenLayerFeedforwardNeuralNetwork(NeuralNetwork):
def __init__(self):
NeuralNetwork.__init__(self)
self.output_node_list = []
self.hidden_node_list = [Node()]
self.input_node_list = []
return
def add_output_node(self):
new_node = OutputNode()
self.output_node_list.append(new_node)
for hidden_node in self.hidden_node_list:
new_node.add_input(hidden_node)
return
def add_input_node(self):
new_input_node = InputNode()
self.input_node_list.append(new_input_node)
for hidden_node in self.hidden_node_list:
hidden_node.add_input(new_input_node)
new_hidden_node = Node()
self.hidden_node_list.append(new_hidden_node)
for output_node in self.output_node_list:
output_node.add_input(new_hidden_node)
for input_node in self.input_node_list:
new_hidden_node.add_input(input_node)
return
"""
计算均方误差
"""
def mean_squared_error(self, labels):
sum_ = 0.0
for index in range(0, len(labels), 1):
sum_ += math.pow((self.output_node_list[index].recent_output - labels[index]), 2)
return sum_ / 2
def set_input(self, value_list):
assert len(value_list) == len(self.input_node_list)
for index in range(0, len(value_list), 1):
value = value_list[index]
node = self.input_node_list[index]
node.set_input_val(value)
return
def reset(self):
for input_node in self.input_node_list:
input_node.activated = False
for hidden_node in self.hidden_node_list:
hidden_node.activated = False
for output_node in self.output_node_list:
output_node.activated = False
return
def output_gradient_item(self, labels):
g = []
for index in range(0, len(self.output_node_list), 1):
output_node = self.output_node_list[index]
label = labels[index]
g.append(output_node.recent_output * (1 - output_node.recent_output) * (label - output_node.recent_output))
return g
def hidden_gradient_item(self, g):
e = []
for index in range(0, len(self.hidden_node_list), 1):
e.append(0.0)
for output_node_index in range(0, len(self.output_node_list), 1):
output_node = self.output_node_list[output_node_index]
for index in range(0, len(output_node.input_list), 1):
weight = output_node.input_list[index][1]
e[index] += (weight * g[output_node_index])
for index in range(0, len(self.hidden_node_list), 1):
hidden_node = self.hidden_node_list[index]
e[index] *= (hidden_node.recent_output * (1 - hidden_node.recent_output))
return e
def adjust(self, labels):
g = self.output_gradient_item(labels)
e = self.hidden_gradient_item(g)
for index in range(0, len(self.output_node_list), 1):
output_node = self.output_node_list[index]
output_node.threshold += - self.eta * g[index]
for hidden_input_pair in output_node.input_list:
hidden_input_pair[1] += self.eta * g[index] * hidden_input_pair[0].recent_output
for index in range(0, len(self.hidden_node_list), 1):
hidden_node = self.hidden_node_list[index]
hidden_node.threshold += - self.eta * e[index]
for initial_input_pair in hidden_node.input_list:
initial_input_pair[1] += self.eta * e[index] * initial_input_pair[0].recent_output
return
def run(self):
for data_item in self.data_set:
self.reset()
self.set_input(data_item.feature_vector)
result_item = []
for output_node in self.output_node_list:
result_item.append(output_node.output_())
print result_item + data_item.label
self.adjust(data_item.label)
return
file_handler = open('E://data/ann/train_1.txt')
data_set = []
line = file_handler.readline()
while line:
record = Record()
item_feature_vector = []
str_list = line.split()
item_feature_vector.append(float(str_list[0]))
item_feature_vector.append(float(str_list[1]))
record.feature_vector = item_feature_vector
record.label = [float(str_list[2])]
data_set.append(record)
line = file_handler.readline()
print len(data_set)
sfn = SingleHiddenLayerFeedforwardNeuralNetwork()
sfn.add_input_node()
sfn.add_input_node()
sfn.add_output_node()
sfn.set_data_set(data_set)
for index in range(0, 30, 1):
sfn.run()
又另外写了一个Python脚本来生成训练数据，其实就是一个分布在(0,1)之间的函数：
"""
用于生成 f(x,y) = x^2 - 0.59x + 0.47y + 0.13
"""
def quadratic_data_gen(file_path, data_scale):
file_handler = open(file_path, mode='w')
for index in range(0, data_scale, 1):
x = random.random()
y = random.random()
f = (x * x - 0.59 * x + 0.47 * y + 0.13)
line = '%f %f %f\n' % (x, y, f)
file_handler.write(line)
file_handler.close()
return
quadratic_data_gen('E://data/ann/train_1.txt', 15000)
15000条数据跑了30遍后，效果似乎不是太好。
左边是神经网络输出，右边是标记。