代码来源：《Python神经网络编程》
手写数据集下载地址: 1.训练数据集 2.测试数据集
摘要
本文代码主要讲解基于Python的简单神经网络构建用于识别手写数据集，类模块具有通用性，在分析清楚问题后可以加以改动，运用于其他方面。
代码
import
numpy
# scipy.special for the sigmoid function expit()
import
scipy
.
special
import
matplotlib
.
pyplot
as
plt
# neural network class definition
class
neuralNetwork
:
# initialise the neural network
def
__init__
(
self
,
inputnodes
,
hiddennodes
,
outputnodes
,
learningrate
)
:
# set number of nodes in each input, hidden, output layer
self
.
inodes
=
inputnodes
self
.
hnodes
=
hiddennodes
self
.
onodes
=
outputnodes
# link weight matrices, wih and who
# weight inside the arrays are w_i_j, where link is from node i to node j in the next layer
# w11 w21
# w12 w22 etc
# 创建的两个链接权重矩阵
# self.wih = (numpy.random.rand(self.hnodes, self.inodes) - 0.5)
# self.who = (numpy.random.rand(self.onodes, self.hnodes) - 0.5)
# 正态分布初始化值，第一个参数表示正态分布中心，第二个参数表示标准方差，第三个参数表示形状
self
.
wih
=
numpy
.
random
.
normal
(
0.0
,
pow
(
self
.
hnodes
,
-
0.5
)
,
(
self
.
hnodes
,
self
.
inodes
)
)
self
.
who
=
numpy
.
random
.
normal
(
0.0
,
pow
(
self
.
onodes
,
-
0.5
)
,
(
self
.
onodes
,
self
.
hnodes
)
)
# learning rate
self
.
lr
=
learningrate
# activation function is the sigmoid function
# 相当于创建一个函数，函数接收x，返回scipy.special.expit(x)，调用时使用self.activation_function(...)即可
self
.
activation_function
=
lambda
x
:
scipy
.
special
.
expit
(
x
)
pass
# train the neural network
def
train
(
self
,
inputs_list
,
targets_list
)
:
# convert inputs list to 2d array
inputs
=
numpy
.
array
(
inputs_list
,
ndmin
=
2
)
.
T
targets
=
numpy
.
array
(
targets_list
,
ndmin
=
2
)
.
T
# calculate signals into hidden layer
hidden_inputs
=
numpy
.
dot
(
self
.
wih
,
inputs
)
# calculate the signals emerging from hidden layer
hidden_outputs
=
self
.
activation_function
(
hidden_inputs
)
# calculate signals into final output layer
final_inputs
=
numpy
.
dot
(
self
.
who
,
hidden_outputs
)
# calculate the signals emerging from final output layer
final_outputs
=
self
.
activation_function
(
final_inputs
)
# error is the (target - actual)
output_errors
=
targets
-
final_outputs
# hidden layer error is the output_errors, split by weights, recombined at hidden nodes
hidden_errors
=
numpy
.
dot
(
self
.
who
.
T
,
output_errors
)
# update the weights for the links between the hidden and output layer
self
.
who
+=
self
.
lr
*
numpy
.
dot
(
(
output_errors
*
final_outputs
*
(
1.0
-
final_outputs
)
)
,
numpy
.
transpose
(
hidden_outputs
)
)
# update the weights for the links between the input and hidden layers
self
.
wih
+=
self
.
lr
*
numpy
.
dot
(
(
hidden_errors
*
hidden_outputs
*
(
1.0
-
hidden_outputs
)
)
,
numpy
.
transpose
(
inputs
)
)
pass
# query the network
def
query
(
self
,
inputs_list
)
:
# convert inputs list to 2d array
# ndmin指定数组最小维度，ndmin=2表示强制将数组转换为2维
inputs
=
numpy
.
array
(
inputs_list
,
ndmin
=
2
)
.
T
# calculate signals into hidden layer
hidden_inputs
=
numpy
.
dot
(
self
.
wih
,
inputs
)
# calculate the signals emerging from hidden layer
hidden_outputs
=
self
.
activation_function
(
hidden_inputs
)
# calculate signals into final output layer
final_inputs
=
numpy
.
dot
(
self
.
who
,
hidden_outputs
)
# calculate the signals emerging from final output layer
final_outputs
=
self
.
activation_function
(
final_inputs
)
return
final_outputs
# number of input, hidden and output nodes
input_nodes
=
784
# 784个输入节点
hidden_nodes
=
200
# 100个隐藏节点
output_nodes
=
10
# 10个输出节点
# learning_rate is 0.5
learning_rate
=
0.1
# create instance of neural network
n
=
neuralNetwork
(
input_nodes
,
hidden_nodes
,
output_nodes
,
learning_rate
)
# load the mnist training data CSV file into a list
training_data_file
=
open
(
"mnist_data/mnist_train.csv"
,
'r'
)
training_data_list
=
training_data_file
.
readlines
(
)
# 读入文件，将之变为一个列表，以行为单位
training_data_file
.
close
(
)
# train the neural network
# epochs is the number of times the training data set is used for training
epochs
=
5
for
e
in
range
(
epochs
)
:
# go through all records in the training data set
for
record
in
training_data_list
:
# split the record by the ',' commas
all_values
=
record
.
split
(
','
)
# scale and shift the inputs
inputs
=
(
numpy
.
asfarray
(
all_values
[
1
:
]
)
/
255.0
*
0.99
)
+
0.01
# 1*784，输入层有784个节点
# create the target output values (all 0.01, except the desired label which is 0.99)
targets
=
numpy
.
zeros
(
output_nodes
)
+
0.01
# all_values[0] is the target label for this record
targets
[
int
(
all_values
[
0
]
)
]
=
0.99
n
.
train
(
inputs
,
targets
)
pass
pass
# test the neural network
test_data_file
=
open
(
"mnist_data/mnist_test.csv"
,
'r'
)
test_data_list
=
test_data_file
.
readlines
(
)
test_data_file
.
close
(
)
# scorecard for how well the network performs, initially empty
scorecard
=
[
]
# go through all the records in the test data set
for
record
in
test_data_list
:
# split the record by the ',' commas
all_values
=
record
.
split
(
','
)
# correct answer is first value
correct_label
=
int
(
all_values
[
0
]
)
print
(
correct_label
,
"correct label"
)
# scale and shift the inputs
inputs
=
(
numpy
.
asfarray
(
all_values
[
1
:
]
)
/
255.0
*
0.99
)
+
0.01
# query the network
outputs
=
n
.
query
(
inputs
)
# the index of the highest value correesponds to the label
label
=
numpy
.
argmax
(
outputs
)
# 返回数组中最大索引值
print
(
label
,
"network's answer"
)
# append correct or incorrect to list
if
label
==
correct_label
:
# network's answer matches correct answer, add 1 to scorecard
scorecard
.
append
(
1
)
else
:
# network's answer doesn't match correct answer, add 0 to scorecard
scorecard
.
append
(
0
)
pass
pass
# calculate the performance score, the fraction of correct answers
scorecard_array
=
numpy
.
asarray
(
scorecard
)
# 将输入转化为数组
print
(
"performance = "
,
scorecard_array
.
sum
(
)
/
scorecard_array
.
size
)
总结
- 网络训练中矩阵计算起到重要作用，要特别注意两个矩阵相乘时的矩阵形状
- sigmoid函数的定义域与值域
- 反向误差传播中计算部分要深入理解，书中的三层网络结构中最后一层输出层在计算式也要使用sigmoid函数
- 在一定程度上多次使用数据集训练网络可以提高识别率
