Neural Net Package Examples
Raphael Cobe
12/13/2017
library("neuralnet")Going to create a neural network to perform square rooting Type ?neuralnet for more information on the neuralnet library
Generate 50 random numbers uniformly distributed between 0 and 100 And store them as a dataframe
traininginput <- as.data.frame(runif(50, min=0, max=100))
trainingoutput <- sqrt(traininginput)Column bind the data into one variable
trainingdata <- cbind(traininginput,trainingoutput)
colnames(trainingdata) <- c("Input","Output")Train the neural network Going to have 10 hidden layers Threshold is a numeric value specifying the threshold for the partial derivatives of the error function as stopping criteria.
net.sqrt <- neuralnet(Output~Input,trainingdata, hidden=10, threshold=0.01)
print(net.sqrt)## $call
## neuralnet(formula = Output ~ Input, data = trainingdata, hidden = 10,
## threshold = 0.01)
##
## $response
## Output
## 1 5.851392717
## 2 8.440391463
## 3 8.638619613
## 4 7.943876919
## 5 6.698937325
## 6 6.904396383
## 7 6.619515757
## 8 4.261340241
## 9 6.467765351
## 10 8.564697284
## 11 9.270867002
## 12 4.355408356
## 13 7.304841019
## 14 0.945039966
## 15 7.167649701
## 16 7.361314205
## 17 5.799598240
## 18 7.410426302
## 19 9.671606009
## 20 8.804359378
## 21 2.104655064
## 22 2.840205043
## 23 8.003080648
## 24 8.553072940
## 25 8.518440947
## 26 9.115074222
## 27 8.467743276
## 28 9.825145959
## 29 8.210314475
## 30 7.149447512
## 31 1.693619472
## 32 2.199430369
## 33 3.214397352
## 34 5.808405826
## 35 9.745618738
## 36 9.076903633
## 37 9.031498766
## 38 6.887047976
## 39 9.309182529
## 40 7.484717453
## 41 1.402485498
## 42 4.159932760
## 43 7.429124889
## 44 4.801393049
## 45 8.931425903
## 46 3.751783226
## 47 8.202653052
## 48 7.780300562
## 49 9.266059234
## 50 9.233962926
##
## $covariate
## [,1]
## [1,] 34.2387967277
## [2,] 71.2402080419
## [3,] 74.6257488150
## [4,] 63.1051805103
## [5,] 44.8757612845
## [6,] 47.6706894115
## [7,] 43.8179888530
## [8,] 18.1590206455
## [9,] 41.8319886317
## [10,] 73.3540395740
## [11,] 85.9489749651
## [12,] 18.9695819514
## [13,] 53.3607023070
## [14,] 0.8931005374
## [15,] 51.3752022292
## [16,] 54.1889468208
## [17,] 33.6353397463
## [18,] 54.9144179793
## [19,] 93.5399628012
## [20,] 77.5167440530
## [21,] 4.4295729371
## [22,] 8.0667646835
## [23,] 64.0492998529
## [24,] 73.1550567085
## [25,] 72.5638361648
## [26,] 83.0845780671
## [27,] 71.7026761966
## [28,] 96.5334931156
## [29,] 67.4092637841
## [30,] 51.1145997327
## [31,] 2.8683469165
## [32,] 4.8374939477
## [33,] 10.3323503397
## [34,] 33.7375782430
## [35,] 94.9770845938
## [36,] 82.3901795549
## [37,] 81.5679699648
## [38,] 47.4314298248
## [39,] 86.6608793614
## [40,] 56.0209953459
## [41,] 1.9669655710
## [42,] 17.3050405690
## [43,] 55.1918966230
## [44,] 23.0533752125
## [45,] 79.7703686636
## [46,] 14.0758773778
## [47,] 67.2835170990
## [48,] 60.5330768274
## [49,] 85.8598537277
## [50,] 85.2660713252
##
## $model.list
## $model.list$response
## [1] "Output"
##
## $model.list$variables
## [1] "Input"
##
##
## $err.fct
## function (x, y)
## {
## 1/2 * (y - x)^2
## }
## <environment: 0x7fc40d39cd40>
## attr(,"type")
## [1] "sse"
##
## $act.fct
## function (x)
## {
## 1/(1 + exp(-x))
## }
## <environment: 0x7fc40d39cd40>
## attr(,"type")
## [1] "logistic"
##
## $linear.output
## [1] TRUE
##
## $data
## Input Output
## 1 34.2387967277 5.851392717
## 2 71.2402080419 8.440391463
## 3 74.6257488150 8.638619613
## 4 63.1051805103 7.943876919
## 5 44.8757612845 6.698937325
## 6 47.6706894115 6.904396383
## 7 43.8179888530 6.619515757
## 8 18.1590206455 4.261340241
## 9 41.8319886317 6.467765351
## 10 73.3540395740 8.564697284
## 11 85.9489749651 9.270867002
## 12 18.9695819514 4.355408356
## 13 53.3607023070 7.304841019
## 14 0.8931005374 0.945039966
## 15 51.3752022292 7.167649701
## 16 54.1889468208 7.361314205
## 17 33.6353397463 5.799598240
## 18 54.9144179793 7.410426302
## 19 93.5399628012 9.671606009
## 20 77.5167440530 8.804359378
## 21 4.4295729371 2.104655064
## 22 8.0667646835 2.840205043
## 23 64.0492998529 8.003080648
## 24 73.1550567085 8.553072940
## 25 72.5638361648 8.518440947
## 26 83.0845780671 9.115074222
## 27 71.7026761966 8.467743276
## 28 96.5334931156 9.825145959
## 29 67.4092637841 8.210314475
## 30 51.1145997327 7.149447512
## 31 2.8683469165 1.693619472
## 32 4.8374939477 2.199430369
## 33 10.3323503397 3.214397352
## 34 33.7375782430 5.808405826
## 35 94.9770845938 9.745618738
## 36 82.3901795549 9.076903633
## 37 81.5679699648 9.031498766
## 38 47.4314298248 6.887047976
## 39 86.6608793614 9.309182529
## 40 56.0209953459 7.484717453
## 41 1.9669655710 1.402485498
## 42 17.3050405690 4.159932760
## 43 55.1918966230 7.429124889
## 44 23.0533752125 4.801393049
## 45 79.7703686636 8.931425903
## 46 14.0758773778 3.751783226
## 47 67.2835170990 8.202653052
## 48 60.5330768274 7.780300562
## 49 85.8598537277 9.266059234
## 50 85.2660713252 9.233962926
##
## $net.result
## $net.result[[1]]
## [,1]
## 1 5.8545706809
## 2 8.4405329478
## 3 8.6411563088
## 4 7.9395240395
## 5 6.7018761901
## 6 6.9053484522
## 7 6.6231075777
## 8 4.2595745330
## 9 6.4723257588
## 10 8.5663504429
## 11 9.2756481901
## 12 4.3519014459
## 13 7.3018850658
## 14 0.9466689648
## 15 7.1659170147
## 16 7.3579222209
## 17 5.8022566481
## 18 7.4066942373
## 19 9.6655016562
## 20 8.8086663009
## 21 2.1067850945
## 22 2.8335081310
## 23 7.9990406055
## 24 8.5545848968
## 25 8.5195307232
## 26 9.1207961072
## 27 8.4682153845
## 28 9.8105072437
## 29 8.2079102171
## 30 7.1478909020
## 31 1.6989799904
## 32 2.1985598167
## 33 3.2174837924
## 34 5.8111562465
## 35 9.7357554404
## 36 9.0826544108
## 37 9.0371960980
## 38 6.8881781922
## 39 9.3134995167
## 40 7.4805482517
## 41 1.3964110464
## 42 4.1602167298
## 43 7.4252737087
## 44 4.7937233469
## 45 8.9367123476
## 46 3.7592176787
## 47 8.2001750211
## 48 7.7754821003
## 49 9.2708916191
## 50 9.2390984265
##
##
## $weights
## $weights[[1]]
## $weights[[1]][[1]]
## [,1] [,2] [,3] [,4]
## [1,] -0.06230735274 -1.51572110901 -0.09727195245 2.58518628586
## [2,] -0.73958607903 0.02809383609 0.06375553541 -0.03070444516
## [,5] [,6] [,7] [,8]
## [1,] -1.09746848283 -1.1536076414 -0.5256476305 1.47356334123
## [2,] -0.03224842736 -0.0335923939 -0.3411163694 -0.08721712414
## [,9] [,10]
## [1,] -1.5925064196 -1.26311160899
## [2,] 0.2836748451 0.02703760589
##
## $weights[[1]][[2]]
## [,1]
## [1,] 2.6531858159
## [2,] -1.7912904088
## [3,] 2.9053698001
## [4,] 2.8361244782
## [5,] -2.6607234446
## [6,] -0.8009277332
## [7,] -0.7514631590
## [8,] -0.2934013306
## [9,] -1.1757085363
## [10,] 1.0272508127
## [11,] 2.7380450170
##
##
##
## $startweights
## $startweights[[1]]
## $startweights[[1]][[1]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -1.132092536 -0.8173301416 0.20311975886 0.9134799612 -1.2231103298
## [2,] -2.665907915 0.6318022294 -0.09094601702 -0.5893173963 -0.3975576421
## [,6] [,7] [,8] [,9] [,10]
## [1,] -1.2517262785 1.1311361857 0.2380446694 -0.9311124457 -0.2951888200
## [2,] -0.4045253703 -0.5853325413 -1.7181460870 0.5153204893 0.9136720094
##
## $startweights[[1]][[2]]
## [,1]
## [1,] 1.2547804557
## [2,] 0.2548977783
## [3,] -0.2660595186
## [4,] 1.4428209510
## [5,] -1.1161662745
## [6,] 0.4540597153
## [7,] 0.4318652721
## [8,] 2.0410791466
## [9,] -0.1438008738
## [10,] -0.4556588264
## [11,] 0.9827354616
##
##
##
## $generalized.weights
## $generalized.weights[[1]]
## [,1]
## 1 -0.0030351386889
## 2 -0.0009546152928
## 3 -0.0008868521133
## 4 -0.0011477023584
## 5 -0.0019361466875
## 6 -0.0017575903102
## 7 -0.0020126332815
## 8 -0.0082858880416
## 9 -0.0021717914257
## 10 -0.0009116163410
## 11 -0.0006949979979
## 12 -0.0077333227947
## 13 -0.0014754179544
## 14 9.1499206058903
## 15 -0.0015636301846
## 16 -0.0014413122756
## 17 -0.0031266460924
## 18 -0.0014126162924
## 19 -0.0005885123014
## 20 -0.0008333009630
## 21 -0.0987958003349
## 22 -0.0345780724823
## 23 -0.0011225200844
## 24 -0.0009155634424
## 25 -0.0009274111640
## 26 -0.0007393366287
## 27 -0.0009450004129
## 28 -0.0005504466328
## 29 -0.0010393342254
## 30 -0.0015759452888
## 31 -0.2543573322246
## 32 -0.0834913919335
## 33 -0.0223452954867
## 34 -0.0031108488479
## 35 -0.0005699780608
## 36 -0.0007504692973
## 37 -0.0007638552451
## 38 -0.0017716691198
## 39 -0.0006843552425
## 40 -0.0013708123137
## 41 -0.6727821959929
## 42 -0.0089530026998
## 43 -0.0014019168245
## 44 -0.0057237458151
## 45 -0.0007939266942
## 46 -0.0127194481055
## 47 -0.0010422841490
## 48 -0.0012210885163
## 49 -0.0006963405911
## 50 -0.0007053449148
##
##
## $result.matrix
## 1
## error 0.0005333657894
## reached.threshold 0.0090926918928
## steps 6064.0000000000000
## Intercept.to.1layhid1 -0.0623073527383
## Input.to.1layhid1 -0.7395860790341
## Intercept.to.1layhid2 -1.5157211090076
## Input.to.1layhid2 0.0280938360945
## Intercept.to.1layhid3 -0.0972719524479
## Input.to.1layhid3 0.0637555354117
## Intercept.to.1layhid4 2.5851862858564
## Input.to.1layhid4 -0.0307044451582
## Intercept.to.1layhid5 -1.0974684828258
## Input.to.1layhid5 -0.0322484273613
## Intercept.to.1layhid6 -1.1536076414094
## Input.to.1layhid6 -0.0335923938987
## Intercept.to.1layhid7 -0.5256476304757
## Input.to.1layhid7 -0.3411163693974
## Intercept.to.1layhid8 1.4735633412332
## Input.to.1layhid8 -0.0872171241387
## Intercept.to.1layhid9 -1.5925064196414
## Input.to.1layhid9 0.2836748450989
## Intercept.to.1layhid10 -1.2631116089948
## Input.to.1layhid10 0.0270376058877
## Intercept.to.Output 2.6531858158710
## 1layhid.1.to.Output -1.7912904088013
## 1layhid.2.to.Output 2.9053698000991
## 1layhid.3.to.Output 2.8361244781609
## 1layhid.4.to.Output -2.6607234445740
## 1layhid.5.to.Output -0.8009277332056
## 1layhid.6.to.Output -0.7514631589929
## 1layhid.7.to.Output -0.2934013306500
## 1layhid.8.to.Output -1.1757085362682
## 1layhid.9.to.Output 1.0272508127290
## 1layhid.10.to.Output 2.7380450169588
##
## attr(,"class")
## [1] "nn"Plot the neural network
plot(net.sqrt, rep = "best")
Test the neural network on some training data
testdata <- as.data.frame((1:10)^2) #Generate some squared numbers
net.results <- compute(net.sqrt, testdata) #Run them through the neural networkLets see what properties net.sqrt has
ls(net.results)## [1] "net.result" "neurons"Lets see the results
print(net.results$net.result)## [,1]
## [1,] 0.995651087
## [2,] 2.004949735
## [3,] 2.997236258
## [4,] 4.003559121
## [5,] 4.992983838
## [6,] 6.004351125
## [7,] 6.999959828
## [8,] 7.995941860
## [9,] 9.005608807
## [10,] 9.971903887Lets display a better version of the results
cleanoutput <- cbind(testdata,sqrt(testdata),
as.data.frame(net.results$net.result))
colnames(cleanoutput) <- c("Input","Expected Output","Neural Net Output")
print(cleanoutput)## Input Expected Output Neural Net Output
## 1 1 1 0.995651087
## 2 4 2 2.004949735
## 3 9 3 2.997236258
## 4 16 4 4.003559121
## 5 25 5 4.992983838
## 6 36 6 6.004351125
## 7 49 7 6.999959828
## 8 64 8 7.995941860
## 9 81 9 9.005608807
## 10 100 10 9.971903887sin function
Generate random data and the dependent variable
x <- sort(runif(50, min = 0, max = 4*pi))
y <- sin(x)
data <- cbind(x,y)Create the neural network responsible for the sin function
library(neuralnet)
sin.nn <- neuralnet(y ~ x, data = data, hidden = 5, stepmax = 100000, learningrate = 10e-6,
act.fct = 'logistic', err.fct = 'sse', rep = 5, lifesign = "minimal",
linear.output = T)## hidden: 5 thresh: 0.01 rep: 1/5 steps: stepmax min thresh: 0.01599376894
## hidden: 5 thresh: 0.01 rep: 2/5 steps: 7943 error: 0.41295 time: 0.73 secs
## hidden: 5 thresh: 0.01 rep: 3/5 steps: 34702 error: 0.02068 time: 3.13 secs
## hidden: 5 thresh: 0.01 rep: 4/5 steps: 4603 error: 0.4004 time: 0.41 secs
## hidden: 5 thresh: 0.01 rep: 5/5 steps: 3582 error: 0.26375 time: 0.34 secs## Warning: algorithm did not converge in 1 of 5 repetition(s) within the
## stepmaxVisualize the neural network
plot(sin.nn, rep = "best")
Generate data for the prediction of the using the neural net;
testdata<- as.data.frame(runif(10, min=0, max=(4*pi)))
testdata## runif(10, min = 0, max = (4 * pi))
## 1 1.564816433
## 2 4.692188270
## 3 10.942269605
## 4 11.432769193
## 5 1.528565797
## 6 4.277983023
## 7 7.863112004
## 8 3.233025098
## 9 4.212822393
## 10 11.584672483Calculate the real value using the sin function
testdata.result <- sin(testdata)Make the prediction
sin.nn.result <- compute(sin.nn, testdata)
sin.nn.result$net.result## [,1]
## [1,] 1.04026644587
## [2,] -0.99122081475
## [3,] -0.77154683268
## [4,] -0.80702735515
## [5,] 1.03394587608
## [6,] -0.91997356615
## [7,] 1.02031970677
## [8,] -0.08226873533
## [9,] -0.89463523567
## [10,] -0.81283835083Compare with the real values:
better <- cbind(testdata, sin.nn.result$net.result, testdata.result, (sin.nn.result$net.result-testdata.result))
colnames(better) <- c("Input", "NN Result", "Result", "Error")
better## Input NN Result Result Error
## 1 1.564816433 1.04026644587 0.99998212049 0.040284325379
## 2 4.692188270 -0.99122081475 -0.99979597259 0.008575157839
## 3 10.942269605 -0.77154683268 -0.99857964177 0.227032809091
## 4 11.432769193 -0.80702735515 -0.90594290260 0.098915547446
## 5 1.528565797 1.03394587608 0.99910842368 0.034837452408
## 6 4.277983023 -0.91997356615 -0.90712021799 -0.012853348159
## 7 7.863112004 1.02031970677 0.99995831846 0.020361388309
## 8 3.233025098 -0.08226873533 -0.09130510334 0.009036368006
## 9 4.212822393 -0.89463523567 -0.87779026852 -0.016844967152
## 10 11.584672483 -0.81283835083 -0.83144207031 0.018603719479Calculate the RMSE:
library(Metrics)
rmse(better$Result, better$`NN Result`)## [1] 0.08095028855Plot the results:
plot(x,y)
plot(sin, 0, (4*pi), add=T)
x1 <- seq(0, 4*pi, by=0.1)
lines(x1, compute(sin.nn, data.frame(x=x1))$net.result, col="green")
A classification problem
Using the iris dataset
data(iris)
iris.dataset <- irisCheck what is inside the dataset:
head(iris.dataset)## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosaChange the dataset so we are able to predict classes:
iris.dataset$setosa <- iris.dataset$Species=="setosa"
iris.dataset$virginica = iris.dataset$Species == "virginica"
iris.dataset$versicolor = iris.dataset$Species == "versicolor"Separate into train and test data:
train <- sample(x = nrow(iris.dataset), size = nrow(iris)*0.5)
train## [1] 116 3 137 124 100 48 28 123 99 54 129 128 96 11 97 115 53
## [18] 8 133 85 91 70 60 45 113 119 69 126 114 86 109 140 58 13
## [35] 77 57 7 61 9 111 141 39 120 98 104 88 83 106 20 147 74
## [52] 122 93 72 73 146 4 38 1 22 118 103 51 21 80 82 25 78
## [69] 148 143 14 50 23 84 40iristrain <- iris.dataset[train,]
irisvalid <- iris.dataset[-train,]
print(nrow(iristrain))## [1] 75print(nrow(irisvalid))## [1] 75Build the Neural Network for the classification:
nn <- neuralnet(setosa+versicolor+virginica ~ Sepal.Length + Sepal.Width, data=iristrain, hidden=3,
rep = 2, err.fct = "ce", linear.output = F, lifesign = "minimal", stepmax = 1000000)## hidden: 3 thresh: 0.01 rep: 1/2 steps: 77918 error: 54.96826 time: 9.41 secs
## hidden: 3 thresh: 0.01 rep: 2/2 steps: 53687 error: 54.24648 time: 6.25 secsLet’s check the neural network that we just built
plot(nn, rep="best")
Let’s try to make the prediction:
comp <- compute(nn, irisvalid[-3:-8])
pred.weights <- comp$net.result
idx <- apply(pred.weights, 1, which.max)
pred <- c('setosa', 'versicolor', 'virginica')[idx]
table(pred, irisvalid$Species)##
## pred setosa versicolor virginica
## setosa 28 0 0
## versicolor 1 13 5
## virginica 0 9 19AND operation
AND <- c(rep(0,3),1)
OR <- c(0,rep(1,3))
binary.data <- data.frame(expand.grid(c(0,1), c(0,1)), AND)
print(net <- neuralnet(AND~Var1+Var2, binary.data, hidden=0, rep=10, err.fct="ce", linear.output=FALSE))## $call
## neuralnet(formula = AND ~ Var1 + Var2, data = binary.data, hidden = 0,
## rep = 10, err.fct = "ce", linear.output = FALSE)
##
## $response
## AND
## 1 0
## 2 0
## 3 0
## 4 1
##
## $covariate
## [,1] [,2]
## [1,] 0 0
## [2,] 1 0
## [3,] 0 1
## [4,] 1 1
##
## $model.list
## $model.list$response
## [1] "AND"
##
## $model.list$variables
## [1] "Var1" "Var2"
##
##
## $err.fct
## function (x, y)
## {
## -(y * log(x) + (1 - y) * log(1 - x))
## }
## <bytecode: 0x7fc40ffe5320>
## <environment: 0x7fc40f694320>
## attr(,"type")
## [1] "ce"
##
## $act.fct
## function (x)
## {
## 1/(1 + exp(-x))
## }
## <bytecode: 0x7fc411aad0b0>
## <environment: 0x7fc40f694320>
## attr(,"type")
## [1] "logistic"
##
## $linear.output
## [1] FALSE
##
## $data
## Var1 Var2 AND
## 1 0 0 0
## 2 1 0 0
## 3 0 1 0
## 4 1 1 1
##
## $net.result
## $net.result[[1]]
## [,1]
## 1 0.000002695358491
## 2 0.012447835011968
## 3 0.012965173560536
## 4 0.983981385389474
##
## $net.result[[2]]
## [,1]
## 1 0.00000315688225
## 2 0.01310670401458
## 3 0.01365089349474
## 4 0.98311464468695
##
## $net.result[[3]]
## [,1]
## 1 0.000003460347827
## 2 0.013260919578620
## 3 0.014209021664229
## 4 0.982449843378523
##
## $net.result[[4]]
## [,1]
## 1 0.000001983238558
## 2 0.010703727902892
## 3 0.011850536824598
## 4 0.984945581601299
##
## $net.result[[5]]
## [,1]
## 1 0.000002596117268
## 2 0.012230765715951
## 3 0.012587604110748
## 4 0.983819270199875
##
## $net.result[[6]]
## [,1]
## 1 0.000008009074861
## 2 0.017574542535434
## 3 0.017074549365727
## 4 0.974874120014102
##
## $net.result[[7]]
## [,1]
## 1 0.00000745379384
## 2 0.01656711199861
## 3 0.01620580785285
## 4 0.97384223062722
##
## $net.result[[8]]
## [,1]
## 1 0.000002908306166
## 2 0.012616292497621
## 3 0.012785233809382
## 4 0.982728419604644
##
## $net.result[[9]]
## [,1]
## 1 0.00000477964004
## 2 0.01484648917102
## 3 0.01521870612542
## 4 0.97988978562439
##
## $net.result[[10]]
## [,1]
## 1 0.000007143257891
## 2 0.016544552786363
## 3 0.016578752614244
## 4 0.975431226286737
##
##
## $weights
## $weights[[1]]
## $weights[[1]][[1]]
## [,1]
## [1,] -12.823976646
## [2,] 8.450294039
## [3,] 8.491538128
##
##
## $weights[[2]]
## $weights[[2]][[1]]
## [,1]
## [1,] -12.665922490
## [2,] 8.344484422
## [3,] 8.385717112
##
##
## $weights[[3]]
## $weights[[3]][[1]]
## [,1]
## [1,] -12.574137986
## [2,] 8.264553670
## [3,] 8.334570734
##
##
## $weights[[4]]
## $weights[[4]][[1]]
## [,1]
## [1,] -13.130777431
## [2,] 8.604375660
## [3,] 8.707316634
##
##
## $weights[[5]]
## $weights[[5]][[1]]
## [,1]
## [1,] -12.861490991
## [2,] 8.469996447
## [3,] 8.499115741
##
##
## $weights[[6]]
## $weights[[6]][[1]]
## [,1]
## [1,] -11.734927292
## [2,] 7.711354230
## [3,] 7.681983027
##
##
## $weights[[7]]
## $weights[[7]][[1]]
## [,1]
## [1,] -11.806779961
## [2,] 7.723150089
## [3,] 7.700732928
##
##
## $weights[[8]]
## $weights[[8]][[1]]
## [,1]
## [1,] -12.747936811
## [2,] 8.387867120
## [3,] 8.401340097
##
##
## $weights[[9]]
## $weights[[9]][[1]]
## [,1]
## [1,] -12.251140540
## [2,] 8.056106480
## [3,] 8.081246298
##
##
## $weights[[10]]
## $weights[[10]][[1]]
## [,1]
## [1,] -11.849334455
## [2,] 7.764319030
## [3,] 7.766418807
##
##
##
## $startweights
## $startweights[[1]]
## $startweights[[1]][[1]]
## [,1]
## [1,] 0.07602335385
## [2,] 1.06109403863
## [3,] 1.17073812795
##
##
## $startweights[[2]]
## $startweights[[2]][[1]]
## [,1]
## [1,] 0.6340775097
## [2,] 1.3552844223
## [3,] 0.4649171120
##
##
## $startweights[[3]]
## $startweights[[3]][[1]]
## [,1]
## [1,] -0.40573798565
## [2,] -0.05624633045
## [3,] -1.84422926563
##
##
## $startweights[[4]]
## $startweights[[4]][[1]]
## [,1]
## [1,] 1.1692225691
## [2,] 1.1116985397
## [3,] -0.4134833657
##
##
## $startweights[[5]]
## $startweights[[5]][[1]]
## [,1]
## [1,] -0.8614909914
## [2,] 0.3175964468
## [3,] -0.5164842595
##
##
## $startweights[[6]]
## $startweights[[6]][[1]]
## [,1]
## [1,] -0.63492729243
## [2,] -0.07264577009
## [3,] 0.22958302743
##
##
## $startweights[[7]]
## $startweights[[7]][[1]]
## [,1]
## [1,] -0.2067799610
## [2,] 1.4339500887
## [3,] -0.9148670724
##
##
## $startweights[[8]]
## $startweights[[8]][[1]]
## [,1]
## [1,] 0.2520631886
## [2,] 0.0986671202
## [3,] 0.4364629771
##
##
## $startweights[[9]]
## $startweights[[9]][[1]]
## [,1]
## [1,] -0.05114054006
## [2,] 1.40022936031
## [3,] -1.13435370244
##
##
## $startweights[[10]]
## $startweights[[10]][[1]]
## [,1]
## [1,] -0.4493344552
## [2,] -1.1144809705
## [3,] 1.6015416869
##
##
##
## $generalized.weights
## $generalized.weights[[1]]
## [,1] [,2]
## [1,] 8.450294039 8.491538128
## [2,] 8.450294039 8.491538128
## [3,] 8.450294039 8.491538128
## [4,] 8.450294039 8.491538128
##
## $generalized.weights[[2]]
## [,1] [,2]
## [1,] 8.344484422 8.385717112
## [2,] 8.344484422 8.385717112
## [3,] 8.344484422 8.385717112
## [4,] 8.344484422 8.385717112
##
## $generalized.weights[[3]]
## [,1] [,2]
## [1,] 8.26455367 8.334570734
## [2,] 8.26455367 8.334570734
## [3,] 8.26455367 8.334570734
## [4,] 8.26455367 8.334570734
##
## $generalized.weights[[4]]
## [,1] [,2]
## [1,] 8.60437566 8.707316634
## [2,] 8.60437566 8.707316634
## [3,] 8.60437566 8.707316634
## [4,] 8.60437566 8.707316634
##
## $generalized.weights[[5]]
## [,1] [,2]
## [1,] 8.469996447 8.499115741
## [2,] 8.469996447 8.499115741
## [3,] 8.469996447 8.499115741
## [4,] 8.469996447 8.499115741
##
## $generalized.weights[[6]]
## [,1] [,2]
## [1,] 7.71135423 7.681983027
## [2,] 7.71135423 7.681983027
## [3,] 7.71135423 7.681983027
## [4,] 7.71135423 7.681983027
##
## $generalized.weights[[7]]
## [,1] [,2]
## [1,] 7.723150089 7.700732928
## [2,] 7.723150089 7.700732928
## [3,] 7.723150089 7.700732928
## [4,] 7.723150089 7.700732928
##
## $generalized.weights[[8]]
## [,1] [,2]
## [1,] 8.38786712 8.401340097
## [2,] 8.38786712 8.401340097
## [3,] 8.38786712 8.401340097
## [4,] 8.38786712 8.401340097
##
## $generalized.weights[[9]]
## [,1] [,2]
## [1,] 8.05610648 8.081246298
## [2,] 8.05610648 8.081246298
## [3,] 8.05610648 8.081246298
## [4,] 8.05610648 8.081246298
##
## $generalized.weights[[10]]
## [,1] [,2]
## [1,] 7.76431903 7.766418807
## [2,] 7.76431903 7.766418807
## [3,] 7.76431903 7.766418807
## [4,] 7.76431903 7.766418807
##
##
## $result.matrix
## 1 2 3
## error 0.04172690808 0.043970973653 0.045370013968
## reached.threshold 0.00939708932 0.009875399079 0.009923244969
## steps 130.00000000000 134.000000000000 126.000000000000
## Intercept.to.AND -12.82397664615 -12.665922490326 -12.574137985647
## Var1.to.AND 8.45029403863 8.344484422316 8.264553669545
## Var2.to.AND 8.49153812795 8.385717111974 8.334570734373
## 4 5 6
## error 0.037853608723 0.041289339635 0.06040774182
## reached.threshold 0.007501829567 0.008640236144 0.00953122099
## steps 144.000000000000 121.000000000000 112.00000000000
## Intercept.to.AND -13.130777430908 -12.861490991386 -11.73492729243
## Var1.to.AND 8.604375659738 8.469996446841 7.71135422991
## Var2.to.AND 8.707316634293 8.499115740543 7.68198302743
## 7 8 9
## error 0.05955786269 0.042989604414 0.050613457477
## reached.threshold 0.00995196152 0.008132854218 0.009959760561
## steps 117.00000000000 131.000000000000 123.000000000000
## Intercept.to.AND -11.80677996105 -12.747936811436 -12.251140540056
## Var1.to.AND 7.72315008875 8.387867120198 8.056106480307
## Var2.to.AND 7.70073292762 8.401340097113 8.081246297563
## 10
## error 0.058283426286
## reached.threshold 0.008561674945
## steps 115.000000000000
## Intercept.to.AND -11.849334455193
## Var1.to.AND 7.764319029501
## Var2.to.AND 7.766418806916
##
## attr(,"class")
## [1] "nn"Now to validate the predictions:
input <- data.frame(expand.grid(c(0,1), c(0,1)))
net.results <- compute(net, input)
cbind(round(net.results$net.result), AND)## AND
## [1,] 0 0
## [2,] 0 0
## [3,] 0 0
## [4,] 1 1