Last updated: 2019-08-19

Checks: 7 0

Knit directory: polymeRID/

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File Version Author Date Message
html d960dc2 goergen95 2019-08-19 included calibration
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html de84a71 goergen95 2019-08-19 large update for website

Cross Validation

Here, we test for the generalization potential of the CNNs trained with the parameters yielding to the highest accuracy results. To this end, we perform a 10-fold cross-validation which is repeated 5 times.

Tab. 1: The ten highest accuracy results for different preprocessing types at varying kernel sizes.
X types kernel loss acc val_loss val_acc
163 163 norm.d2 90 0.2898488 0.8961039 0.8323456 0.9142857
35 35 sg 70 0.2537513 0.9350649 1.3861195 0.9000000
135 135 raw.d2 90 0.1529336 0.9350649 1.5874773 0.9000000
152 152 norm.d1 150 0.1060385 0.9740260 0.8856056 0.9000000

The following code takes the different levels of the input data and applies the same cross-validation to each of the elements. The same folds are used, so that the results can be compared easily.

data = read.csv(file = paste0(ref, "reference_database.csv"), header = TRUE)

kernels = c(90,70,90,150)
folds = 10
repeats = 5
p = 0.5
nOutcome = length(unique(data$class))

dataList = list()

normd2.data = preprocess(data[,1:ncol(data)-1], type = "norm.d2")
normd2.data$class = data$class
dataList[["norm.d2"]] = normd2.data

sg.data = preprocess(data[,1:ncol(data)-1], type = "norm")
sg.data$class = data$class
dataList[["sg"]] = sg.data

rawd2.data = preprocess(data[,1:ncol(data)-1], type = "raw.d2")
rawd2.data$class = data$class
dataList[["raw.d2"]] = rawd2.data

normd1.data = preprocess(data[,1:ncol(data)-1], type = "norm.d1")
normd1.data$class = data$class
dataList[["norm.d1"]] = nnormd1.data


for (i in 1:length(dataList)){
  tmp = dataList[[i]]
  
  # preparing data inputs
  set.seed(42)
  foldIndex = lapply(1:repeats, caret::createDataPartition, y=sg.tmp$class, times = folds, p=p)
  foldIndex = do.call(c,foldIndex)
  
  cvData = list()
  for (rep in 1:repeats){
    rep_Index = foldIndex[(rep*folds-folds+1):(rep*folds)] #always jump to the correct number of folds forward for each repeat
    
    dataFold = lapply(1:folds,function(x){
      
      training = tmp[unlist(rep_Index[x]), ]
      validation = tmp[-unlist(rep_Index[x]), ]
      foldtmp = list(training,validation)
      names(foldtmp) = c("training","validation")
      return(foldtmp)
    })
    cvData[[rep]] = dataFold
  }
  results = data.frame(repeats = rep(0,repeats*folds),
                       fold = rep(0,repeats*folds),
                       loss = rep(0,repeats*folds),
                       acc = rep(0,repeats*folds))
  counter = 1
  for (rep in 1:repeats){
    #print(paste0("Starting repeat ",rep," out of ",repeats,"."))
    for (fold in 1:folds){
      
      variables = ncol(cvData[[rep]][[fold]][[1]])-1
      x_train = cvData[[rep]][[fold]][["training"]][,1:variables]
      y_train = unlist(cvData[[rep]][[fold]][["training"]][1+variables])
      x_test = cvData[[rep]][[fold]][["validation"]][,1:variables]
      y_test = unlist(cvData[[rep]][[fold]][["validation"]][1+variables])
      
      # function to get keras array for dataframes
      K <- keras::backend()
      df_to_karray <- function(df){
        tmp = as.matrix(df)
        tmp = K$expand_dims(tmp, axis = 2L)
        tmp = K$eval(tmp)
      }
      
      # 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)
      
      # fitting the model
      kernelMod = prepNNET(kernel, variables, nOutcome = nOutcome)
      historyMod =  keras::fit(kernelMod, x = x_train, y = y_train,
                               epochs=300,
                               batch_size = 10 )
      
      evalK = keras::evaluate(kernelMod, x=x_test, y=y_test)
      results$repeats[counter] = rep
      results$fold[counter] = fold
      results$loss[counter] = evalK$loss
      results$acc[counter] = evalK$acc
      print(results[counter,])
      counter = counter + 1
      write.csv(results, file = paste0(output,"nnet/cv/cvResults_K",kernel,".csv"))
    }
  }
}

We can now retrive information about the accurcies for the complete cross-validation process by calculating averages accross the accuracy values.

results = data.frame(type=c("norm.d2","sg","raw.d2","norm.d1"), accuracy = rep(0,4))
results$accuracy[1] = round(mean(results.normd2$acc),3)
results$accuracy[2] = round(mean(results.sg$acc),3)
results$accuracy[3] = round(mean(results.rawd2$acc),3)
results$accuracy[4] = round(mean(results.normd1$acc),3)
results = results[order(-results$accuracy),]
Tab. 2: Results of the repeated cross-valiation for different preprocessing types.
type accuracy
3 raw.d2 0.868
1 norm.d2 0.846
2 sg 0.839
4 norm.d1 0.830

With an accuracy of approximatley 0.87 the use of the second derivative of the raw data yielded to the highes accuracy value when calculated in a cross-validation approach. With 0.85 the second derivateve of the normalized data yielded to the second highest accuracy.


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] tensorflow_1.14.0         abind_1.4-5              
 [3] e1071_1.7-2               keras_2.2.4.1            
 [5] workflowr_1.4.0.9001      baseline_1.2-1           
 [7] gridExtra_2.3             stringr_1.4.0            
 [9] prospectr_0.1.3           RcppArmadillo_0.9.600.4.0
[11] openxlsx_4.1.0.1          magrittr_1.5             
[13] ggplot2_3.2.0             reshape2_1.4.3           
[15] dplyr_0.8.3              

loaded via a namespace (and not attached):
 [1] reticulate_1.13  tidyselect_0.2.5 xfun_0.8         purrr_0.3.2     
 [5] lattice_0.20-38  colorspace_1.4-1 generics_0.0.2   htmltools_0.3.6 
 [9] yaml_2.2.0       base64enc_0.1-3  rlang_0.4.0      pillar_1.4.2    
[13] glue_1.3.1       withr_2.1.2      foreach_1.4.7    plyr_1.8.4      
[17] munsell_0.5.0    gtable_0.3.0     zip_2.0.3        codetools_0.2-16
[21] evaluate_0.14    knitr_1.24       SparseM_1.77     tfruns_1.4      
[25] class_7.3-15     highr_0.8        Rcpp_1.0.2       scales_1.0.0    
[29] backports_1.1.4  jsonlite_1.6     fs_1.3.1         digest_0.6.20   
[33] stringi_1.4.3    grid_3.6.1       rprojroot_1.3-2  tools_3.6.1     
[37] lazyeval_0.2.2   tibble_2.1.3     crayon_1.3.4     whisker_0.3-2   
[41] pkgconfig_2.0.2  zeallot_0.1.0    Matrix_1.2-17    assertthat_0.2.1
[45] rmarkdown_1.14   iterators_1.0.12 R6_2.4.0         git2r_0.26.1    
[49] compiler_3.6.1