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全连接神经网络是深度学习的基础，理解它就可以掌握深度学习的核心概念：前向传播、反向误差传递、权重、学习率等。这里先用python创建模型，用minist作为数据集进行训练。

定义3层神经网络：输入层节点28*28(对应minist图片像素数)、隐藏层节点300、输出层节点10(对应0-9个数字)。

网络的激活函数采用sigmoid，网络权重的初始化采用正态分布。

完整代码如下：

1 #-*- coding:utf-8 -*-

2

3 u"""全连接神经网络训练学习MINIST"""

4

5 __author__ = 'zhengbiqing 460356155@qq.com'

6

7

8 importnumpy9 importscipy.special10 importscipy.misc11 from PIL importImage12 importmatplotlib.pyplot13 importpylab14 importdatetime15 from random importshuffle16

17

18 #是否训练网络

19 LEARN =True20

21 #是否保存网络

22 SAVE_PARA =False23

24 #网络节点数

25 INPUT = 784

26 HIDDEN = 300

27 OUTPUT = 10

28

29 #学习率和训练次数

30 LR = 0.05

31 EPOCH = 10

32

33 #训练数据集文件

34 TRAIN_FILE = 'mnist_train.csv'

35 TEST_FILE = 'mnist_test.csv'

36

37 #网络保存文件名

38 WEIGHT_IH = "minist_fc_wih.npy"

39 WEIGHT_HO = "minist_fc_who.npy"

40

41

42 #神经网络定义

43 classNeuralNetwork:44 def __init__(self, inport_nodes, hidden_nodes, output_nodes, learnning_rate):45 #神经网络输入层、隐藏层、输出层节点数

46 self.inodes =inport_nodes47 self.hnodes =hidden_nodes48 self.onodes =output_nodes49

50 #神经网络训练学习率

51 self.learnning_rate =learnning_rate52

53 #用均值为0，标准方差为连接数的-0.5次方的正态分布初始化权重

54 #权重矩阵行列分别为hidden * input、 output * hidden，和ih、ho相反

55 self.wih = numpy.random.normal(0.0, pow(self.hnodes, -0.5), (self.hnodes, self.inodes))56 self.who = numpy.random.normal(0.0, pow(self.onodes, -0.5), (self.onodes, self.hnodes))57

58 #sigmoid函数为激活函数

59 self.active_fun = lambdax: scipy.special.expit(x)60

61 #设置神经网络权重，在加载已训练的权重时调用

62 defset_weight(self, wih, who):63 self.wih =wih64 self.who =who65

66 #前向传播，根据输入得到输出

67 defget_outputs(self, input_list):68 #把list转换为N * 1的矩阵，ndmin=2二维，T转制

69 inputs = numpy.array(input_list, ndmin=2).T70

71 #隐藏层输入 = W dot X，矩阵乘法

72 hidden_inputs =numpy.dot(self.wih, inputs)73 hidden_outputs =self.active_fun(hidden_inputs)74

75 final_inputs =numpy.dot(self.who, hidden_outputs)76 final_outputs =self.active_fun(final_inputs)77

78 returninputs, hidden_outputs, final_outputs79

80 #网络训练，误差计算，误差反向分配更新网络权重

81 deftrain(self, input_list, target_list):82 inputs, hidden_outputs, final_outputs =self.get_outputs(input_list)83

84 targets = numpy.array(target_list, ndmin=2).T85

86 #误差计算

87 output_errors = targets -final_outputs88 hidden_errors =numpy.dot(self.who.T, output_errors)89

90 #连接权重更新

91 self.who += numpy.dot(self.learnning_rate * output_errors * final_outputs * (1 -final_outputs), hidden_outputs.T)92 self.wih += numpy.dot(self.learnning_rate * hidden_errors * hidden_outputs * (1 -hidden_outputs), inputs.T)93

94

95 #图像像素值变换

96 defvals2input(vals):97 #[0,255]的图像像素值转换为i[0.01,1]，以便sigmoid函数作非线性变换

98 return (numpy.asfarray(vals) / 255.0 * 0.99) + 0.01

99

100

101 '''

102 训练网络103 train：是否训练网络，如果不训练则直接加载已训练得到的网络权重104 epoch：训练次数105 save：是否保存训练结果，即网络权重106 '''

107 defnet_train(train, epochs, save):108 iftrain:109 with open(TRAIN_FILE, 'r') as train_file:110 train_list =train_file.readlines()111

112 for epoch inrange(epochs):113 #打乱训练数据

114 shuffle(train_list)115

116 for data intrain_list:117 all_vals = data.split(',')118 #图像数据为0～255，转换到0.01～1区间，以便激活函数更有效

119 inputs = vals2input(all_vals[1:])120

121 #标签，正确的为0.99，其他为0.01

122 targets = numpy.zeros(OUTPUT) + 0.01

123 targets[int(all_vals[0])] = 0.99

124

125 net.train(inputs, targets)126

127 #每个epoch结束后用测试集检查识别准确度

128 net_test(epoch)129 print('')130

131 ifsave:132 #保存连接权重

133 numpy.save(WEIGHT_IH, net.wih)134 numpy.save(WEIGHT_HO, net.who)135 else:136 #不训练直接加载已保存的权重

137 wih =numpy.load(WEIGHT_IH)138 who =numpy.load(WEIGHT_HO)139 net.set_weight(wih, who)140

141

142 '''

143 用测试集检查准确率144 '''

145 defnet_test(epoch):146 with open(TEST_FILE, 'r') as test_file:147 test_list =test_file.readlines()148

149 ok =0150 errlist = [0] * 10

151

152 for data intest_list:153 all_vals = data.split(',')154 inputs = vals2input(all_vals[1:])155 _, _, net_out =net.get_outputs(inputs)156

157 max =numpy.argmax(net_out)158 if max ==int(all_vals[0]):159 ok += 1

160 else:161 #识别错误统计，每个数字识别错误计数

162 #print('target:', all_vals[0], 'net_out:', max)

163 errlist[int(all_vals[0])] += 1

164

165 print('EPOCH: {epoch} score: {score}'.format(epoch=epoch, score = ok / len(test_list) * 100))166 print('error list:', errlist, 'total:', sum(errlist))167

168

169 #变换图片的尺寸，保存变换后的图片

170 defresize_img(filein, fileout, width, height, type):171 img =Image.open(filein)172 out =img.resize((width, height), Image.ANTIALIAS)173 out.save(fileout, type)174

175

176 #用训练得到的网络识别一个图片文件

177 defimg_test(img_file):178 file_name_list = img_file.split('.')179 file_name, file_type = file_name_list[0], file_name_list[1]180 out_file = file_name + 'out' + '.' +file_type181 resize_img(img_file, out_file, 28, 28, file_type)182

183 img_array = scipy.misc.imread(out_file, flatten=True)184 img_data = 255.0 - img_array.reshape(784)185 img_data = (img_data / 255.0 * 0.99) + 0.01

186

187 _, _, net_out =net.get_outputs(img_data)188 max =numpy.argmax(net_out)189 print('pic recognized as:', max)190

191

192 #显示数据集某个索引对应的图片

193 defimg_show(train, index):194 file = TRAIN_FILE if train elseTEST_FILE195 with open(file, 'r') as test_file:196 test_list =test_file.readlines()197

198 all_values = test_list[index].split(',')199 print('number is:', all_values[0])200

201 image_array = numpy.asfarray(all_values[1:]).reshape((28, 28))202 matplotlib.pyplot.imshow(image_array, cmap='Greys', interpolation='None')203 pylab.show()204

205

206 start_time =datetime.datetime.now()207

208 net =NeuralNetwork(INPUT, HIDDEN, OUTPUT, LR)209 net_train(LEARN, EPOCH, SAVE_PARA)210

211 if notLEARN:212 net_test(0)213 else:214 print('MINIST FC Train:', INPUT, HIDDEN, OUTPUT, 'LR:', LR, 'EPOCH:', EPOCH)215 print('train spend time:', datetime.datetime.now() -start_time)216

217 #用画图软件创建图片文件，由得到的网络进行识别

218 #img_test('t9.png')

219

220 #显示minist中的某个图片

221 #img_show(True, 1)

784-300-10简单的全连接神经网络训练结果准确率基本在97.7%左右，运行结果如下：

EPOCH: 0 score: 95.96000000000001

error list:  [13, 21, 31, 28, 51, 61, 33, 66, 44, 56]  total:  404

EPOCH: 1 score: 96.77

error list:  [15, 19, 27, 63, 37, 37, 21, 40, 18, 46]  total:  323

EPOCH: 2 score: 97.25

error list:  [9, 17, 26, 26, 24, 56, 21, 41, 22, 33]  total:  275

EPOCH: 3 score: 97.82

error list:  [9, 16, 21, 18, 20, 18, 22, 21, 31, 42]  total:  218

EPOCH: 4 score: 97.54

error list:  [12, 23, 17, 25, 15, 34, 19, 25, 22, 54]  total:  246

EPOCH: 5 score: 97.78999999999999

error list:  [10, 16, 20, 23, 21, 32, 18, 31, 26, 24]  total:  221

EPOCH: 6 score: 97.6

error list:  [9, 13, 26, 34, 27, 26, 20, 28, 22, 35]  total:  240

EPOCH: 7 score: 97.74000000000001

error list:  [12, 8, 26, 29, 27, 26, 25, 20, 27, 26]  total:  226

EPOCH: 8 score: 97.77

error list:  [7, 10, 27, 16, 29, 28, 23, 29, 26, 28]  total:  223

EPOCH: 9 score: 97.99

error list:  [11, 10, 32, 17, 18, 24, 14, 22, 21, 32]  total:  201

MINIST FC Train: 784 300 10 LR: 0.05 EPOCH: 10

train spend time:  0:05:54.137925

Process finished with exit code 0