R语言神经网络与深度学习（一）

#R语言神经网络与深度学习（一）

#画出ReLU函数

x=seq(-1,1,0.1)   #生成x变量，赋值-1~1等差数列

relu=function(x) ifelse(x>0,x,0)   #定义relu函数

plot(x,relu(x),type="l")   #画出函数

text(0.6,0.4,"ReLU(x)")    #添加文字说明

#感知器模型

install.packages("neuralnet")   #神经网络基本包

library(neuralnet)

#先看一个神经网络完成非线性回归的例子

traininginput=as.data.frame(runif(50,min = 1,max = 100))#生成1~100之间的50个随机数作为训练输入

trainingoutput=log(traininginput)

traindata=cbind(traininginput,trainingoutput) #按列绑定输入输出构成训练集

colnames(traindata)=c("input","output")  #设定训练数据的属性名

#网络包含输入层+隐层+输出层，隐层带有10个神经元

#指定损失函数阈值0.01

net.log=neuralnet(output~input,traindata,hidden = 10,threshold = 0.01)

print(net.log) #输出结果非常丰富，包含列神经网络各层结点之间的权重，以及拟合效果等

$call

neuralnet(formula = output ~ input, data = traindata, hidden = 10,

    threshold = 0.01)

 

$response

      output

1  3.7636802

2  4.4644749

3  1.7436266

4  4.4739950

5  4.5343469

6  4.3922093

7  3.1241007

8  4.1268159

9  4.5423753

10 4.0774836

11 4.0416826

12 4.5609231

13 1.9013686

14 4.0447385

15 3.9645057

16 4.2647878

17 4.1592951

18 4.0911714

19 4.1509276

20 4.0576335

21 4.3243332

22 3.9223834

23 0.2055446

24 3.7957673

25 4.5556668

26 4.0531594

27 3.7693452

28 4.0053732

29 2.7642808

30 3.8549792

31 2.9460532

32 2.6809099

33 2.9693048

34 3.9097673

35 4.3624009

36 3.8901353

37 3.7667034

38 2.9365815

39 4.6030032

40 4.5424663

41 4.6006236

42 4.4700970

43 4.2985708

44 4.6039118

45 2.4092103

46 3.8176258

47 2.1870567

48 4.4869113

49 4.3311433

50 4.4543536

 

$covariate

              

 [1,] 43.106777

 [2,] 86.875399

 [3,]  5.718043

 [4,] 87.706411

 [5,] 93.162653

 [6,] 80.818776

 [7,] 22.739436

 [8,] 61.980258

 [9,] 93.913611

[10,] 58.996821

[11,] 56.922039

[12,] 95.671757

[13,]  6.695051

[14,] 57.096255

[15,] 52.694217

[16,] 71.149822

[17,] 64.026377

[18,] 59.809912

[19,] 63.492872

[20,] 57.837277

[21,] 75.515146

[22,] 50.520712

[23,]  1.228194

[24,] 44.512379

[25,] 95.170192

[26,] 57.579083

[27,] 43.351669

[28,] 54.892306

[29,] 15.867625

[30,] 47.227636

[31,] 19.030695

[32,] 14.598370

[33,] 19.478373

[34,] 49.887342

[35,] 78.445248

[36,] 48.917503

[37,] 43.237292

[38,] 18.851293

[39,] 99.783536

[40,] 93.922153

[41,] 99.546369

[42,] 87.365201

[43,] 73.594536

[44,] 99.874243

[45,] 11.125173

[46,] 45.496064

[47,]  8.908953

[48,] 88.846600

[49,] 76.031160

[50,] 86.000542

 

$model.list

$model.list$response

[1] "output"

 

$model.list$variables

[1] "input"

 

 

$err.fct

function (x, y)

{

    1/2 * (y - x)^2

}

attr(,"type")

[1] "sse"

 

$act.fct

function (x)

{

    1/(1 + exp(-x))

}

attr(,"type")

[1] "logistic"

 

$linear.output

[1] TRUE

 

$data

       input    output

1  43.106777 3.7636802

2  86.875399 4.4644749

3   5.718043 1.7436266

4  87.706411 4.4739950

5  93.162653 4.5343469

6  80.818776 4.3922093

7  22.739436 3.1241007

8  61.980258 4.1268159

9  93.913611 4.5423753

10 58.996821 4.0774836

11 56.922039 4.0416826

12 95.671757 4.5609231

13  6.695051 1.9013686

14 57.096255 4.0447385

15 52.694217 3.9645057

16 71.149822 4.2647878

17 64.026377 4.1592951

18 59.809912 4.0911714

19 63.492872 4.1509276

20 57.837277 4.0576335

21 75.515146 4.3243332

22 50.520712 3.9223834

23  1.228194 0.2055446

24 44.512379 3.7957673

25 95.170192 4.5556668

26 57.579083 4.0531594

27 43.351669 3.7693452

28 54.892306 4.0053732

29 15.867625 2.7642808

30 47.227636 3.8549792

31 19.030695 2.9460532

32 14.598370 2.6809099

33 19.478373 2.9693048

34 49.887342 3.9097673

35 78.445248 4.3624009

36 48.917503 3.8901353

37 43.237292 3.7667034

38 18.851293 2.9365815

39 99.783536 4.6030032

40 93.922153 4.5424663

41 99.546369 4.6006236

42 87.365201 4.4700970

43 73.594536 4.2985708

44 99.874243 4.6039118

45 11.125173 2.4092103

46 45.496064 3.8176258

47  8.908953 2.1870567

48 88.846600 4.4869113

49 76.031160 4.3311433

50 86.000542 4.4543536

 

$exclude

NULL

 

$net.result

$net.result[[1]]

           [,1]

 [1,] 3.7611324

 [2,] 4.4676382

 [3,] 1.7450071

 [4,] 4.4767355

 [5,] 4.5333355

 [6,] 4.3973251

 [7,] 3.1264467

 [8,] 4.1283555

 [9,] 4.5407127

[10,] 4.0778398

[11,] 4.0412524

[12,] 4.5576071

[13,] 1.9011417

[14,] 4.0443723

[15,] 3.9627180

[16,] 4.2694251

[17,] 4.1616376

[18,] 4.0918471

[19,] 4.1530636

[20,] 4.0575438

[21,] 4.3296645

[22,] 3.9200950

[23,] 0.2058114

[24,] 3.7930785

[25,] 4.5528409

[26,] 4.0529725

[27,] 3.7667663

[28,] 4.0042391

[29,] 2.7649095

[30,] 3.8522756

[31,] 2.9476404

[32,] 2.6810941

[33,] 2.9710108

[34,] 3.9073649

[35,] 4.3677722

[36,] 3.8875888

[37,] 3.7641387

[38,] 2.9381196

[39,] 4.5951146

[40,] 4.5407961

[41,] 4.5930255

[42,] 4.4730158

[43,] 4.3036824

[44,] 4.5959112

[45,] 2.4079249

[46,] 3.8148925

[47,] 2.1852585

[48,] 4.4890086

[49,] 4.3365084

[50,] 4.4579205

 

 

$weights

$weights[[1]]

$weights[[1]][[1]]

           [,1]     [,2]     [,3]       [,4]        [,5]

[1,] 0.44219842 3.240757 3.202168 -0.7877108  0.40986679

[2,] 0.03712114 3.187768 1.834951  0.1106201 -0.02969351

            [,6]       [,7]      [,8]       [,9]    [,10]

[1,] -0.63775130  0.3209541  1.088130 -1.7936935 2.897821

[2,]  0.02159582 -0.2508112 -1.443933  0.7005957 3.665216

 

$weights[[1]][[2]]

             [,1]

 [1,]  0.97762799

 [2,]  1.18062819

 [3,] -0.66380527

 [4,] -0.01894856

 [5,]  1.22171422

 [6,] -0.94174505

 [7,]  1.95836189

 [8,] -1.71540135

 [9,] -1.58353932

[10,]  0.49503450

[11,] -0.11677912

 

 

 

$generalized.weights

$generalized.weights[[1]]

               [,1]

 [1,] -0.0022210615

 [2,] -0.0007116606

 [3,] -0.1330105041

 [4,] -0.0006983659

 [5,] -0.0006173567

 [6,] -0.0008171924

 [7,] -0.0066323721

 [8,] -0.0012800595

 [9,] -0.0006070058

[10,] -0.0013815810

[11,] -0.0014591160

[12,] -0.0005834740

[13,] -0.0863911855

[14,] -0.0014523614

[15,] -0.0016390983

[16,] -0.0010236995

[17,] -0.0012162685

[18,] -0.0013528213

[19,] -0.0012324843

[20,] -0.0014241447

[21,] -0.0009238604

[22,] -0.0017459440

[23,]  4.5417733837

[24,] -0.0021141160

[25,] -0.0005900886

[26,] -0.0014338833

[27,] -0.0022017184

[28,] -0.0015414536

[29,] -0.0129830198

[30,] -0.0019321744

[31,] -0.0092002434

[32,] -0.0152801351

[33,] -0.0088113650

[34,] -0.0017792936

[35,] -0.0008631226

[36,] -0.0018325209

[37,] -0.0022107137

[38,] -0.0093639779

[39,] -0.0005320635

[40,] -0.0006068891

[41,] -0.0005348975

[42,] -0.0007037923

[43,] -0.0009663184

[44,] -0.0005309836

[45,] -0.0266392482

[46,] -0.0020447419

[47,] -0.0432961417

[48,] -0.0006805536

[49,] -0.0009128212

[50,] -0.0007259494

 

 

$startweights

$startweights[[1]]

$startweights[[1]][[1]]

            [,1]      [,2]      [,3]      [,4]       [,5]

[1,] -0.03350376 0.2343721 0.9467223 0.6239159 -0.4009166

[2,]  0.18488311 0.5129832 0.3752907 0.2825048 -0.6657770

           [,6]       [,7]       [,8]      [,9]      [,10]

[1,] -0.5012463 -0.5600915  0.9140493 -1.970049 -0.1085638

[2,]  0.1647918 -1.1582757 -1.4669017  1.260016  0.6588312

 

$startweights[[1]][[2]]

            [,1]

 [1,]  0.6881827

 [2,]  0.7268674

 [3,] -0.9532505

 [4,] -0.3083938

 [5,]  0.9051658

 [6,] -0.2535406

 [7,]  0.7907308

 [8,] -0.2203825

 [9,]  1.0148172

[10,]  0.2076412

[11,] -0.4062244

 

 

 

$result.matrix

                                [,1]

error                   2.551317e-04

reached.threshold       8.599877e-03

steps                   1.757000e+03

Intercept.to.1layhid1   4.421984e-01

input.to.1layhid1       3.712114e-02

Intercept.to.1layhid2   3.240757e+00

input.to.1layhid2       3.187768e+00

Intercept.to.1layhid3   3.202168e+00

input.to.1layhid3       1.834951e+00

Intercept.to.1layhid4  -7.877108e-01

input.to.1layhid4       1.106201e-01

Intercept.to.1layhid5   4.098668e-01

input.to.1layhid5      -2.969351e-02

Intercept.to.1layhid6  -6.377513e-01

input.to.1layhid6       2.159582e-02

Intercept.to.1layhid7   3.209541e-01

input.to.1layhid7      -2.508112e-01

Intercept.to.1layhid8   1.088130e+00

input.to.1layhid8      -1.443933e+00

Intercept.to.1layhid9  -1.793694e+00

input.to.1layhid9       7.005957e-01

Intercept.to.1layhid10  2.897821e+00

input.to.1layhid10      3.665216e+00

Intercept.to.output     9.776280e-01

1layhid1.to.output      1.180628e+00

1layhid2.to.output     -6.638053e-01

1layhid3.to.output     -1.894856e-02

1layhid4.to.output      1.221714e+00

1layhid5.to.output     -9.417451e-01

1layhid6.to.output      1.958362e+00

1layhid7.to.output     -1.715401e+00

1layhid8.to.output     -1.583539e+00

1layhid9.to.output      4.950345e-01

1layhid10.to.output    -1.167791e-01

 

attr(,"class")

[1] "nn"

ls(net.log)  #得到神经网络包含等属性，并且可以通过net.log$XXX直接访问内容

[1] "act.fct"             "call"               

 [3] "covariate"           "data"               

 [5] "err.fct"             "exclude"            

 [7] "generalized.weights" "linear.output"      

 [9] "model.list"          "net.result"         

[11] "response"            "result.matrix"      

[13] "startweights"        "weights"            

net.log$act.fct  #查看act.fct属性的结果，激活函数默认sigmoid

function (x) 

{

    1/(1 + exp(-x))

}

attr(,"type")

[1] "logistic"

 

plot(net.log)   #画出神经网络

 

#神经网络计算效果案例

testdata=as.data.frame((1:10)^2)  #测试能否准确计算一个数的对数值

 net.result=compute(net.log,testdata)  #输入测试数据，让训练好的神经网络完成运算

ls(net.result)  #显示运算结果

[1] "net.result" "neurons"   

 net.results=compute(net.log,testdata)  #输入测试数据，让训练好的神经网络完成运算

 ls(net.results)  #显示运算结果

[1] "net.result" "neurons"   

 #为了方便比较，把实际值和神经网络计算的值列一起

niceoutput=cbind(testdata,log(testdata),as.data.frame(net.results$net.result))

 colnames(niceoutput)=c("input","expected output","neural net output")  #输出结果列命名

 print(niceoutput) #打印出结果

   input expected output neural net output

1      1        0.000000        0.03171921

2      4        1.386294        1.39359903

3      9        2.197225        2.19541861

4     16        2.772589        2.77326131

5     25        3.218876        3.22133011

6     36        3.583519        3.58289693

7     49        3.891820        3.88928457

8     64        4.158883        4.16121537

9     81        4.394449        4.39953416

10   100        4.605170        4.59701350

 #还可以计算实际值与预测值差（误差）的均方差

 error=as.data.frame(net.results$net.result)-log(testdata) #得到预测误差

mse=sum((error)^2)/nrow(error)   #计算均方误差

 mse   #展示结果，误差均方很小，预测非常准

[1] 0.0001173849