Last updated: 2019-08-15
Checks: 6 1
Knit directory: polymeRID/
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Interesting stuff about CNNs.
Unlike with the random forest and support vector machines, here we did not test for noise in the dataset. This is mainly due to limitations in computation time. The computation time was significantly reduced by installing the keras package in GPU mode based on the CUDA library of Nvidia. Interested readers in setting up a local machine for GPU computations with the R implementation of keras are refered to the About section of this website. Still, CNNs remain computational intensive, since depending on the architecture severel thousands of weights have to be trained. Here, we developed a simple two-block architecture of 4 convolutional layers in total. The number of filters, or feature extractors, increases with each layer by a factor of 2. We choose a rather ‘deep’ network architechture with 4 layers and only small numbers of filters. The code below defines a function to set up and compile a CNN for a given kernel size.
# expects that you have installed keras and tensorflow properly
library(keras)
buildCNN <- function(kernel, nVariables, nOutcome){
model = keras_model_sequential()
model %>%
# block 1
layer_conv_1d(filters = 8,
kernel_size = kernel,
input_shape = c(nVariables,1),
name = "block1_conv1",) %>%
layer_activation_relu(name="block1_relu1") %>%
layer_conv_1d(filters = 16,
kernel_size = kernel,
name = "block1_conv2") %>%
layer_activation_relu(name="block1_relu2") %>%
layer_max_pooling_1d(strides=2,
pool_size = 5,
name="block1_max_pool1") %>%
# block 2
layer_conv_1d(filters = 32,
kernel_size = kernel,
name = "block2_conv1") %>%
layer_activation_relu(name="block2_relu1") %>%
layer_conv_1d(filters = 64,
kernel_size = kernel,
name = "block2_conv2") %>%
layer_activation_relu(name="block2_relu2") %>%
layer_max_pooling_1d(strides=2,
pool_size = 5,
name="block2_max_pool1") %>%
# exit block
layer_global_max_pooling_1d(name="exit_max_pool") %>%
layer_dropout(rate=0.5) %>%
layer_dense(units = nOutcome, activation = "softmax")
# we compile for a classification with the categorcial crossentropy loss function
# and use adam as optimizer function
compile(model, loss="categorical_crossentropy", optimizer="adam", metrics="accuracy")
}The function expects three arguments as input. The first is the kernel size which specifies the width of the window which extracts features from the input data and subsequent layer outputs. Note that the kernel size is held constant throught the network. The second argument expects in integer representing the number of variables of the input which relates to the amount of wavenumbers in the present case. The third argument also expects an integer only this time it is the number of desired output classes. Each convolutional layer as associated with a RelU-activation function. At the end of each block we added a max pooling layer with stride = 2 which takes the maximum values of its respective input and discards unneeded observations effectvly reducing the feature space by half. The exit block again consits of a global max pooling layer and is followed by a dropout layer which randomly silences half of the neurons to reduce the influence of overfitting. The last layer is a fully-connected layer which maps its input to nOutcome classes via the softmax activation function. The last line of code compiles the model so it is ready for training. We use categorical crossentropy as the loss function in our network because currently we have 14 different classes which perfectly fit for one-hot-encoding. If the number of classes is too high, for example in speech recognition problems, sparse categorical crossentropy would be the loss function of choice. As an optimizer function we chose adam as it ensures that the learning rate and decay react adaptive during training. Finally, we tell the model to optimize the training process based on overall accuracy. Let’s build a model and take a look at its parameters:
model = buildCNN(kernel = 50, nVariables = 1863, nOutcome = 12)
modelModel
Model: "sequential"
___________________________________________________________________________
Layer (type) Output Shape Param #
===========================================================================
block1_conv1 (Conv1D) (None, 1814, 8) 408
___________________________________________________________________________
block1_relu1 (ReLU) (None, 1814, 8) 0
___________________________________________________________________________
block1_conv2 (Conv1D) (None, 1765, 16) 6416
___________________________________________________________________________
block1_relu2 (ReLU) (None, 1765, 16) 0
___________________________________________________________________________
block1_max_pool1 (MaxPooling1D) (None, 881, 16) 0
___________________________________________________________________________
block2_conv1 (Conv1D) (None, 832, 32) 25632
___________________________________________________________________________
block2_relu1 (ReLU) (None, 832, 32) 0
___________________________________________________________________________
block2_conv2 (Conv1D) (None, 783, 64) 102464
___________________________________________________________________________
block2_relu2 (ReLU) (None, 783, 64) 0
___________________________________________________________________________
block2_max_pool1 (MaxPooling1D) (None, 390, 64) 0
___________________________________________________________________________
exit_max_pool (GlobalMaxPooling1 (None, 64) 0
___________________________________________________________________________
dropout (Dropout) (None, 64) 0
___________________________________________________________________________
dense (Dense) (None, 12) 780
===========================================================================
Total params: 135,700
Trainable params: 135,700
Non-trainable params: 0
___________________________________________________________________________In total, the current network consists of 135,830 weights to be trained. In the output shape column we can observe the shape transformation of the input data from a 1D-array of size 1814 after the first convolutional layer with 8 filters to an 1D-output of shape 12. We can now take a look how the model performs on our data. But first we need to tranform the input data to arrays which can be understand by the keras::fit() function. We use keras-backend functionality for this.
data = read.csv(file = paste0(ref, "reference_database.csv"), header = TRUE)
K <- keras::backend()
x_train = as.matrix(data[,1:ncol(data)-1])
x = K$expand_dims(x_train, axis = 2L)
x_train = K$eval(x)
y_train = keras::to_categorical(as.numeric(data$class)-1, length(unique(data$class)))
history = keras::fit(model, x = x_train, y = y_train,
epochs=300,
batch_size = 10)
history
plot(history)Trained on 147 samples (batch_size=10, epochs=300)
Final epoch (plot to see history):
loss: 0.05043
acc: 0.9796 set.seed() function before splitting the data. This way all different combinations of kernels and data transformation actually trains and evaluates on the exact same data set. This would not be valid if the generalization potential of the model was going to be assesed. But since we are interested in the performance of different kernel sizes and data transformation techniques it actually is beneficial for comparison if the different models train on the same data. Otherwise, it would not be possible to accout variations in performance either to the parameters or just because a different training and validation set was used.
kernels = c(10,20,30,40,50,60,70,80,90,100,125,150,175,200)
types = c("raw","norm","sg","sg.norm","raw.d1")
results = data.frame(types = rep(0, length(kernels) * length(types)),
kernel =rep(0, length(kernels) * length(types)),
loss = rep(0, length(kernels) * length(types)),
acc = rep(0, length(kernels) * length(types)),
val_loss=rep(0, length(kernels) * length(types)),
val_acc=rep(0, length(kernels) * length(types)))
variables = ncol(data)-1
counter = 1
for (type in types){
if (type == "raw"){
tmp = data
variables = ncol(data)-1
}else{
tmp = preprocess(data[ ,1:ncol(data)-1], type = type)
variables = ncol(tmp)
tmp$class =data$class
}
for (kernel in kernels){
# splitting between training and test
set.seed(42)
index = caret::createDataPartition(y=tmp$class,p=.5)
training = tmp[index$Resample1,]
validation = tmp[-index$Resample1,]
# splitting predictors and labels
x_train = training[,1:variables]
y_train = training[,1+variables]
x_test = validation[,1:variables]
y_test = validation[,1+variables]
#number of preditors and unique targets
nOutcome = length(levels(y_train))
# function to get keras array for dataframes
K <- keras::backend()
df_to_karray <- function(df){
d = as.matrix(df)
d = K$expand_dims(d, axis = 2L)
d = K$eval(d)
}
# coerce data to keras structure
x_train = df_to_karray(x_train)
x_test = df_to_karray(x_test)
y_train = keras::to_categorical(as.numeric(y_train)-1,nOutcome)
y_test = keras::to_categorical(as.numeric(y_test)-1,nOutcome)
# contstruction of "large" neural network
model = prepNNET(kernel, variables, nOutcome)
history = keras::fit(model, x = x_train, y = y_train,
epochs=200, validation_data = list(x_test,y_test),
#callbacks = callback_tensorboard(paste0(output,"nnet/logs")),
batch_size = 10 )
results$types[counter] = type
results$kernel[counter] = kernel
results$loss[counter] = history$metrics$loss[100]
results$acc[counter] = history$metrics$acc[100]
results$val_loss[counter] = history$metrics$val_loss[100]
results$val_acc[counter] = history$metrics$val_acc[100]
write.csv(results, file = paste0(output,"nnet/kernels.csv"))
counter = counter + 1
}
print(results)
}We now can plot the results with increasing kernel sizes on the x-axis, accuracy values for the validation data set on the x-axis and different lines for data transformations.
library(ggplot2)
library(plotly)
kernelPlot = ggplot(data = results, aes(x = kernel, y = val_acc))+
geom_line(aes(color=types,group=types), size = 1.5)+
ylab("validation accuracy")+
xlab("kernel size")+
theme_minimal()
ggplotly(kernelPlot)kernelAcc = aggregate(val_acc ~ kernel, results, mean)
kernelAcc = kernelAcc[order(-kernelAcc$val_acc), ]
type = results[which(results$kernel == kernelAcc$kernel[1]),]
type = type[order(-type$val_acc), ]| kernel | val_acc | |
|---|---|---|
| 7 | 70 | 0.8285714 |
| 6 | 60 | 0.8228571 |
| 3 | 30 | 0.8171429 |
| 2 | 20 | 0.8171429 |
| 5 | 50 | 0.8085714 |
| 8 | 80 | 0.8057143 |
| 10 | 100 | 0.8057143 |
| 9 | 90 | 0.8000000 |
| 4 | 40 | 0.7828571 |
| 13 | 175 | 0.7800000 |
| 11 | 125 | 0.7742857 |
| 1 | 10 | 0.7628571 |
| 12 | 150 | 0.7600000 |
| 14 | 200 | 0.7514286 |
| X | types | kernel | loss | acc | val_loss | val_acc | |
|---|---|---|---|---|---|---|---|
| 35 | 35 | sg | 70 | 0.2537513 | 0.9350649 | 1.3861195 | 0.9000000 |
| 21 | 21 | norm | 70 | 0.0427878 | 0.9870130 | 0.9719612 | 0.8428571 |
| 49 | 49 | sg.norm | 70 | 0.1419386 | 0.9610389 | 0.8783187 | 0.8142857 |
| 7 | 7 | raw | 70 | 0.3521424 | 0.8311688 | 0.9944996 | 0.8000000 |
| 63 | 63 | raw.d1 | 70 | 0.4158809 | 0.8311688 | 0.8798401 | 0.7857143 |
On average, a kernel size of 70 delivered the highest accuracy values yielding to an accuracy of 0.83. For this kernel size the Savitzkiy-Golay smoothed data set yielded to the highest accuracy of 0.90. We will thus proceed to work the smoothed data and a kernel size of 70.
sessionInfo()R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Linux Mint 19.1
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=de_DE.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] plotly_4.9.0 tensorflow_1.14.0
[3] abind_1.4-5 e1071_1.7-2
[5] keras_2.2.4.1 workflowr_1.4.0.9001
[7] baseline_1.2-1 gridExtra_2.3
[9] stringr_1.4.0 prospectr_0.1.3
[11] RcppArmadillo_0.9.600.4.0 openxlsx_4.1.0.1
[13] magrittr_1.5 ggplot2_3.2.0
[15] reshape2_1.4.3 dplyr_0.8.3
loaded via a namespace (and not attached):
[1] httr_1.4.1 tidyr_0.8.3 jsonlite_1.6
[4] viridisLite_0.3.0 foreach_1.4.7 shiny_1.3.2
[7] assertthat_0.2.1 highr_0.8 yaml_2.2.0
[10] pillar_1.4.2 backports_1.1.4 lattice_0.20-38
[13] glue_1.3.1 reticulate_1.13 digest_0.6.20
[16] promises_1.0.1 colorspace_1.4-1 htmltools_0.3.6
[19] httpuv_1.5.1 Matrix_1.2-17 plyr_1.8.4
[22] pkgconfig_2.0.2 SparseM_1.77 purrr_0.3.2
[25] xtable_1.8-4 scales_1.0.0 whisker_0.3-2
[28] later_0.8.0 git2r_0.26.1 tibble_2.1.3
[31] generics_0.0.2 withr_2.1.2 lazyeval_0.2.2
[34] crayon_1.3.4 mime_0.7 evaluate_0.14
[37] fs_1.3.1 class_7.3-15 tools_3.6.1
[40] data.table_1.12.2 munsell_0.5.0 zip_2.0.3
[43] compiler_3.6.1 rlang_0.4.0 grid_3.6.1
[46] iterators_1.0.12 htmlwidgets_1.3 crosstalk_1.0.0
[49] base64enc_0.1-3 labeling_0.3 rmarkdown_1.14
[52] gtable_0.3.0 codetools_0.2-16 R6_2.4.0
[55] tfruns_1.4 knitr_1.24 zeallot_0.1.0
[58] rprojroot_1.3-2 stringi_1.4.3 Rcpp_1.0.2
[61] tidyselect_0.2.5 xfun_0.8