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
html b846f0b goergen95 2019-08-19 Build site.
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Rmd 6bef5e6 goergen95 2019-08-14 confusion matrix output in rf_exploration
html 6bef5e6 goergen95 2019-08-14 confusion matrix output in rf_exploration
html 2385fbc goergen95 2019-08-14 republish for layout change
Rmd 293fd73 goergen95 2019-08-14 first step on svm_exploration
html 293fd73 goergen95 2019-08-14 first step on svm_exploration
Rmd 8b6e72a goergen95 2019-08-14 update rf_exploration
html 8b6e72a goergen95 2019-08-14 update rf_exploration
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Overview

Random Forest (RF) is a machine learning algorithm which is based on the traditional concept of decision trees. It’s popular implementation was developed by Breiman (2001). It represents an ensemble classifier which has been reported to be the primary choice between different ensemble classifiers due to its easy handling and high classification accuracies (Sagi and Rokach 2018). It represents a non-parametric classification method. At each split of a given tree a random number variables are used for the decision of how to split the input data. In the case of RF, a user specified number of trees is grown. The final class decision for an observation is made by a simple majority vote from all trees in the forest. Internal accuracy assessment of the RF classifier traditionally is obtained through an out-of-bag (OOB) error estimation. Here, we kept the number of trees fixed at 500 since above that threshold no substantial gain in accuracy was observed.

Adding Noise

The modality of the data presented to RF is of high importance here. Different levels of data preprocessing might emphasize different features of the patterns to be learned by an algorithm. To grasp this, different transformations of the data were presented to the RF algorithm. Additionally, the raw data signal was jittered to test which transformation might prove beneficial in delivering high classification accuracies even in the presence of noise. To test this, we define a function which adds noise to the raw data and returns a list with the number of elements equal to the levels of noise applied.

addNoise = function(data, levels = c(0), category="class"){
  data.return = list()
  index = which(names(data) == category)
  for (n in levels){
    tmp = as.matrix(data[ , -index])
    if (n == 0){
      tmp = data
    }else{
      tmp = as.data.frame(jitter(tmp, n))
      tmp[category] = data[category]
    }
    data.return[[paste("noise", n, sep="")]] = tmp
  }
  return(data.return)
}

data = read.csv(file = paste0(ref, "reference_database.csv"), header = TRUE)
noisy_data = addNoise(data, levels = c(0,10,100,250,500), category = "class")

# indivitual elements can be selected by using [[ and refering to the index or the name
head(noisy_data[["noise100"]])[1:3,1:3]
  wvn3992.63003826141 wvn3990.70123147964 wvn3988.77242469788
1        -0.010328834          0.01829306         0.001603137
2         0.005237827          0.01683373        -0.013921331
3        -0.011751581          0.01958805         0.002650597

Data Preprocessing

Then, in another function which uses the noisy_data objected as input specified data transformations are applied. These are normalization which centers and scales the input data, as well as different forms of the Savitzkiy-Golay filter (Savitzky and Golay 1964) and first and second derivative of a raw spectrum. The function iterates through the noise level elements in the noisy_data object and returns each specified transformation in a list element below the noise level. The exemplary function below applies the preprocessing for normalization, standard filtering and first derivative only. The implementation of the function used in the project can be found here.

createTrainingSet = function(data, category = "class",
                             SGpara = list(p=3,w=11), lag = 15){
  
  data.return = list()
  for (noise in names(data)){
    
    tmp = as.data.frame(data[[noise]])
    classes = tmp[,category]
    tmp = tmp[!names(tmp) %in% category]
    
    # original data
    data.return[[noise]][["raw"]] = as.data.frame(data[[noise]])
    
    # normalised data
    data_norm = preprocess(tmp, type="norm")
    data_norm[category] = classes
    data.return[[noise]][["norm"]] = data_norm
    
    # SG-filtered data
    data_sg = preprocess(tmp, type="sg", SGpara = SGpara)
    data_sg[category] = classes
    data.return[[noise]][["sg"]] = data_sg
    
    # first derivative of original data
    data_rawd1 = preprocess(tmp, type="raw.d1", lag = lag)
    data_rawd1[category] = classes
    data.return[[noise]][["raw.d1"]] = data_rawd1
    
  }
  return(data.return)
}

# applying the function
test_dataset = createTrainingSet(noisy_data, category = "class")

# individual transformations at a certain noise level can be accessed with [[
head(test_dataset[["noise500"]][["raw.d1"]])[1:3,1:3]
  wvn3963.69793653488 wvn3961.76912975311 wvn3959.84032297134
1          0.08295627          0.02234302          0.17399975
2          0.04253842          0.07918397          0.03849980
3         -0.05579848          0.11670539          0.02503375

Dimensionality Reduction

The data base of Primpke et al. (2018) currently shows 1863 variables for each observations. Most of these data points do not hold relevant information to distinguish between different types of particles. To shorten the computation time, one can use dimensionality reduction techniques such as principal component analysis (PCA). PCA also has been used to transform spectral data of micro-plastics in marine ecosystems before (Jung et al. 2018; Lorenzo-Navarro et al. 2018). PCA basically takes the input data for a given number of observation and by performing a orthogonal transformation to the data transforms these possible correlated variables to uncorrelated principal components. This way, both redundancies in the data as well as possible noise can be accounted for. PCA previously has been successfully applied to FTIR-spectrometer data (Hori and Sugiyama 2003; Nieuwoudt et al. 2004; Mueller et al. 2013; Ami, Mereghetti, and Maria 2013; Fu, Toyoda, and Ihara 2014). Simultaneously, the number of variables can be significantly reduced by applying PCA and thus speeding up the training process. Below we will apply a PCA to the raw data as an example only.

library(factoextra)
tmp = test_dataset[["noise0"]][["raw"]]
pca = prcomp(tmp[ ,-1864]) # omitting class variable
var_info = factoextra::get_eigenvalue(pca)
# setting a threshold of 99% explained variance
threshold = 99
thresInd = which(var_info$cumulative.variance.percent>=threshold)[1]
pca_data = pca$x[,1:thresInd]

We can use the index variable thresInd we just defined to take a look upon all the principal components which explain 99% of the variance in the data set.

eigenvalue variance.percent cumulative.variance.percent
Dim.1 1.5618496 57.7479523 57.74795
Dim.2 0.3875503 14.3293173 72.07727
Dim.3 0.2226548 8.2324559 80.30973
Dim.4 0.1823539 6.7423696 87.05209
Dim.5 0.0897978 3.3201919 90.37229
Dim.6 0.0538395 1.9906665 92.36295
Dim.7 0.0443676 1.6404525 94.00341
Dim.8 0.0324243 1.1988595 95.20227
Dim.9 0.0297937 1.1015939 96.30386
Dim.10 0.0215566 0.7970366 97.10090
Dim.11 0.0173647 0.6420450 97.74294
Dim.12 0.0145994 0.5397977 98.28274
Dim.13 0.0113917 0.4211964 98.70394
Dim.14 0.0069264 0.2560972 98.96003
Dim.15 0.0042735 0.1580104 99.11804

We effectively reduced the number of variables from 1683 to 15 which still bear 99% of the variance we can find in the original data set. However, when it comes to machine learning, it is important to realize that this new data set is not fit to be used in a training process. If we now randomly split the observations into training and test, we effectively mix up these two sets because information of the test set has already influenced the outcome of the PCA. Therefor, the data set need to be split beforehand of the PCA. The analysis is done on the training data only and then the same orthogonal transformations will be applied to the test data. This way it can be ensured that the test set is truly independent from the training process.

Cross Validation

We apply a 10-fold cross-validation which is repeated 5 times. The following code takes a complete data set as input, applies a splitting function from the caret package and then builds the PCA upon the the test set and finally applies the same transformation to the test set. We apply it for the raw data only. Also, we randomly split the data to 50% training and 50% test.

folds = 10
repeats = 5
split_percentage = 0.5
threshold = 99
tmp = test_dataset[["noise0"]][["raw"]]

set.seed(42) # ensure reproducibility
fold_index = lapply(1:repeats, caret::createDataPartition, y=tmp$class,
                   times = folds, p = split_percentage)
fold_index = do.call(c, fold_index)

pcaData = list()
for (rep in 1:repeats){
  rep_index = fold_index[(rep*folds-folds+1):(rep*folds)] # jumps to the correct number of folds forward in each repeat
  
  pcadata_fold = lapply(1:folds,function(x){
    
    # splitting for current fold
    training = tmp[unlist(rep_index[x]),]
    validation = tmp[-unlist(rep_index[x]),]
    
    # keep response
    responseTrain = training$class
    responseVal = validation$class
    
    # apply PCA
    pca = prcomp(training[,1:1863])
    varInfo = factoextra::get_eigenvalue(pca)
    thresInd = which(varInfo$cumulative.variance.percent >= threshold)[1]
    pca_training = pca$x[ ,1:thresInd]
    pca_validation = predict(pca, validation)[ ,1:thresInd]
    
    training = as.data.frame(pca_training)
    training$response = responseTrain
    validation = as.data.frame(pca_validation)
    validation$response = responseVal
    foldtmp = list(training, validation)
    names(foldtmp) = c("training","validation")
    return(foldtmp)
  })
  names(pcadata_fold) = paste("fold", 1:folds, sep ="")
  pcaData[[paste0("repeat",rep)]] = pcadata_fold
}

We now have a list object with the number of elements equivalent to the repeats. Below each repeat element we can access the individual folds. There we find two elements which we can access by referring to "training" and "testing".

pcaData[["repeat5"]][["fold10"]][["training"]][1:3,1:3]
         PC1        PC2         PC3
1 -0.4779164 -0.7786770 -0.02761266
2 -0.4869471 -0.7181236 -0.02492981
4 -0.4661699 -0.7463479 -0.11424932
pcaData[["repeat5"]][["fold10"]][["validation"]][1:3,1:3]
         PC1        PC2         PC3
3 -0.5240744 -0.5931111  0.05961383
5 -0.4718366 -0.6995376 -0.09273887
7 -0.5255215 -0.5928214  0.05184969
summary(pcaData[["repeat5"]][["fold10"]][["training"]]$response)
FIBRE   FUR  HDPE  LDPE    PA    PE   PES   PET    PP    PS   PUR  WOOD 
   14    12     5     6     7     4     8     5     6     4     4     2 
summary(pcaData[["repeat5"]][["fold10"]][["validation"]]$response)
FIBRE   FUR  HDPE  LDPE    PA    PE   PES   PET    PP    PS   PUR  WOOD 
   13    11     5     5     7     4     7     4     6     3     3     2 

Parameter Tuning

For the RF algorithm only the parameter mtry needs a search pattern since we hold the number of trees constant at a value of 500. mtry effectively specifies the number of variables to look at each split within a tree. We took the square root of the number of variables divided by 3 as the first mtry value, the square root itself as the second and the maximum number of variables as a third value. The optimal parameter is then selected to build the final model and it is evaluated with the test data.

training = pcaData[["repeat1"]][["fold1"]][["training"]]
validation =pcaData[["repeat1"]][["fold1"]][["validation"]]
x_train = training[ ,1:ncol(training)-1]
y_train = training$response
x_test = validation[ ,1:ncol(validation)-1]
y_test = validation$response


first = floor(sqrt(ncol(x_train)))/3
if(first <= 1) first <- 1
second = floor(sqrt(ncol(x_train)))
last = ncol(x_train)
mtries = c(first,second,last)

Mods = lapply(1:length(mtries),function(x){return(0)})
accuracy = c()
for (mtry in mtries){
  Mods[which(mtries == mtry)] = list(randomForest::randomForest(x_train, 
                                                                y_train, 
                                                                ntree=500,
                                                                mtry=mtry))
  
  pred = predict(Mods[[which(mtries==mtry)]], x_test)
  conf = caret::confusionMatrix(pred, y_test)
  accuracy = c(accuracy, conf$overall["Kappa"])
}

best_model = Mods[[which(accuracy == max(accuracy))[1]]]
prediction = predict(best_model, x_test)
confMat = caret::confusionMatrix(prediction, y_test)
print(confMat$table)
          Reference
Prediction FIBRE FUR HDPE LDPE PA PE PES PET PP PS PUR WOOD
     FIBRE     8   0    0    0  0  0   0   0  0  0   0    1
     FUR       2  11    0    0  0  0   0   0  0  0   0    0
     HDPE      0   0    3    0  0  0   0   0  0  0   0    0
     LDPE      0   0    0    5  0  0   0   0  0  0   0    0
     PA        0   0    0    0  7  0   0   0  0  0   0    0
     PE        0   0    1    0  0  4   0   0  0  0   0    0
     PES       0   0    0    0  0  0   6   0  0  0   0    0
     PET       0   0    1    0  0  0   1   4  0  0   0    0
     PP        0   0    0    0  0  0   0   0  6  0   0    0
     PS        0   0    0    0  0  0   0   0  0  3   0    0
     PUR       0   0    0    0  0  0   0   0  0  0   3    0
     WOOD      3   0    0    0  0  0   0   0  0  0   0    1

This process of splitting the data set into training and test was automated by putting the above code in a function which can be found here. Finally, we can apply this function to the different levels of prepossessing which were discussed before.

source("code/functions.R")
wavenumbers = readRDS(paste0(ref,"wavenumbers.rds"))
# add noise to data
noisyData = addNoise(data,levels = c(0,10,100,250,500), category = "class")

# preprocessing
testDataset = createTrainingSet(noisyData, category = "class",
                                SGpara = list(p=3, w=11), lag=15,
                                type = c("raw", "norm", "sg", "sg.d1", "sg.d2",
                                  "sg.norm", "sg.norm.d1", "sg.norm.d2",
                                  "raw.d1", "raw.d2", "norm.d1", "norm.d2"))


types = names(testDataset[[1]])

levels = lapply(names(testDataset), function(x){
  rep(x, length(types))
})
levels = unlist(levels)

results = data.frame(level=levels,type = types, kappa = rep(0,length(levels)))

for (level in unique(levels)){
  for (type in types){

    print(paste0("Level: ",level," Type: ",type))
    tmpData = testDataset[[level]][[type]]
    tmpData[which(wavenumbers<=2420 & wavenumbers>=2200)] = 0 # setting C02 window to 0
    tmpModel = pcaCV(tmpData, folds = 10, repeats = 5, threshold = 99, metric = "Kappa", p=0.5, method="rf")
    saveRDS(tmpModel,file = paste0(output,"rf/model_",level,"_",type,"_",round(tmpModel[[1]],2),".rds"))
    results[which(results$level==level & results$type==type),"kappa"] = as.numeric(tmpModel[[1]])
    print(results)

  }
}
saveRDS(paste0(output,"rf/exploration.rds"))

Results

We can now take a look at the kappa scores the algorithm achieved during training for different representations of the data at increasing noise levels.

We can observe that with higher noise ratios the kappa score is reduced significantly. However, there are some data transformations which are able to maintain a relatively high level of accuracy even in the presence of noise. One of the best might be the simple Savitzkiy-Golay filter, as well as the same filter applied to the normalized data. Equal robust results are observed for the raw and the normalized data. The other transformations do not show the same level of robustness to noise. We can look at this more mathematically by calculating the average slopes of the data transformations methods and order the data frame from low to high slopes. Note that we only take the kappa score at noise level 0 and 500 to calculate the average slope.

noise0 = results[results$level == "noise0", ]
noise500 = results[results$level == "noise500", ]
slopes = noise500$kappa - noise0$kappa 
types = unique(results$type)
df = data.frame(type = types, slope = slopes, row.names = NULL)
df = df[order(-slopes),]
type slope
3 sg -0.1249425
6 sg.norm -0.1589274
1 raw -0.2333635
2 norm -0.2954945
9 raw.d1 -0.4136018
10 raw.d2 -0.5027853
4 sg.d1 -0.6313268
5 sg.d2 -0.6585208
8 sg.norm.d2 -0.8103958
7 sg.norm.d1 -0.8190748

We can now confirm, that the average decrease in kappa score is the lowest for the Savitzkiy-Golay filter applied to the raw and the normalized data followed by the raw and the normalized data. The numbers can be interpreted as the loss in Kappa score when the noise level increases from 0 to 500.

Citations on this page

Ami, Diletta, Paolo Mereghetti, and Silvia Maria. 2013. “Multivariate Analysis for Fourier Transform Infrared Spectra of Complex Biological Systems and Processes.” Multivariate Analysis in Management, Engineering and the Sciences. https://doi.org/10.5772/53850.

Breiman, L. 2001. “Random forests.” Machine Learning 45 (1): 5–32. https://doi.org/10.1023/A:1010933404324.

Fu, Yongwei, Kiyohiko Toyoda, and Ikko Ihara. 2014. “Application of ATR-FTIR spectroscopy and principal component analysis in characterization of 15-acetyldeoxynivalenol in corn oil.” Engineering in Agriculture, Environment and Food 7 (4). Elsevier: 163–68. https://doi.org/10.1016/j.eaef.2014.07.001.

Hori, Ritsuko, and Junji Sugiyama. 2003. “A combined FT-IR microscopy and principal component analysis on softwood cell walls.” Carbohydrate Polymers 52 (4): 449–53. https://doi.org/10.1016/S0144-8617(03)00013-4.

Jung, Melissa R., F. David Horgen, Sara V. Orski, Viviana Rodriguez C., Kathryn L. Beers, George H. Balazs, T. Todd Jones, et al. 2018. “Validation of ATR FT-IR to identify polymers of plastic marine debris, including those ingested by marine organisms.” Marine Pollution Bulletin 127 (December 2017). Elsevier: 704–16. https://doi.org/10.1016/j.marpolbul.2017.12.061.

Lorenzo-Navarro, Javier, Modesto Castrillón-Santana, May Gómez, Alicia Herrera, and Pedro A Marín-Reyes. 2018. “Automatic Counting and Classification of Microplastic Particles.” https://doi.org/10.5220/0006725006460652.

Mueller, Daniela, Marco Flôres Ferrão, Luciano Marder, Adilson Ben da Costa, and Rosana de Cássia de Souza Schneider. 2013. “Fourier transform infrared spectroscopy (FTIR) and multivariate analysis for identification of different vegetable oils used in biodiesel production.” Sensors (Switzerland) 13 (4): 4258–71. https://doi.org/10.3390/s130404258.

Nieuwoudt, Helene H., Bernard A. Prior, Isak S. Pretorius, Marena Manley, and Florian F. Bauer. 2004. “Principal component analysis applied to Fourier transform infrared spectroscopy for the design of calibration sets for glycerol prediction models in wine and for the detection and classification of outlier samples.” Journal of Agricultural and Food Chemistry 52 (12): 3726–35. https://doi.org/10.1021/jf035431q.

Primpke, Sebastian, Marisa Wirth, Claudia Lorenz, and Gunnar Gerdts. 2018. “Reference database design for the automated analysis of microplastic samples based on Fourier transform infrared (FTIR) spectroscopy.” Analytical and Bioanalytical Chemistry 410 (21). Analytical; Bioanalytical Chemistry: 5131–41. https://doi.org/10.1007/s00216-018-1156-x.

Sagi, Omer, and Lior Rokach. 2018. “Ensemble learning: A survey.” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 8 (4): 1–18. https://doi.org/10.1002/widm.1249.

Savitzky, Abraham, and Marcel J.E. Golay. 1964. “Smoothing and Differentiation of Data by Simplified Least Squares Procedures.” Analytical Chemistry 36 (8): 1627–39. https://doi.org/10.1021/ac60214a047.


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              knitr_1.24               
 [3] factoextra_1.0.5          tensorflow_1.14.0        
 [5] abind_1.4-5               e1071_1.7-2              
 [7] keras_2.2.4.1             workflowr_1.4.0.9001     
 [9] baseline_1.2-1            gridExtra_2.3            
[11] stringr_1.4.0             prospectr_0.1.3          
[13] RcppArmadillo_0.9.600.4.0 openxlsx_4.1.0.1         
[15] magrittr_1.5              ggplot2_3.2.0            
[17] reshape2_1.4.3            dplyr_0.8.3              

loaded via a namespace (and not attached):
 [1] httr_1.4.1          tidyr_0.8.3         viridisLite_0.3.0  
 [4] jsonlite_1.6        splines_3.6.1       foreach_1.4.7      
 [7] prodlim_2018.04.18  shiny_1.3.2         assertthat_0.2.1   
[10] stats4_3.6.1        highr_0.8           yaml_2.2.0         
[13] ggrepel_0.8.1       ipred_0.9-9         pillar_1.4.2       
[16] backports_1.1.4     lattice_0.20-38     glue_1.3.1         
[19] reticulate_1.13     digest_0.6.20       promises_1.0.1     
[22] randomForest_4.6-14 colorspace_1.4-1    recipes_0.1.6      
[25] httpuv_1.5.1        htmltools_0.3.6     Matrix_1.2-17      
[28] plyr_1.8.4          timeDate_3043.102   pkgconfig_2.0.2    
[31] SparseM_1.77        caret_6.0-84        xtable_1.8-4       
[34] purrr_0.3.2         scales_1.0.0        whisker_0.3-2      
[37] later_0.8.0         gower_0.2.1         lava_1.6.5         
[40] git2r_0.26.1        tibble_2.1.3        generics_0.0.2     
[43] withr_2.1.2         nnet_7.3-12         lazyeval_0.2.2     
[46] mime_0.7            survival_2.44-1.1   crayon_1.3.4       
[49] evaluate_0.14       fs_1.3.1            nlme_3.1-140       
[52] MASS_7.3-51.4       class_7.3-15        tools_3.6.1        
[55] data.table_1.12.2   munsell_0.5.0       zip_2.0.3          
[58] compiler_3.6.1      rlang_0.4.0         grid_3.6.1         
[61] iterators_1.0.12    htmlwidgets_1.3     crosstalk_1.0.0    
[64] labeling_0.3        base64enc_0.1-3     rmarkdown_1.14     
[67] gtable_0.3.0        ModelMetrics_1.2.2  codetools_0.2-16   
[70] R6_2.4.0            tfruns_1.4          lubridate_1.7.4    
[73] zeallot_0.1.0       rprojroot_1.3-2     stringi_1.4.3      
[76] Rcpp_1.0.2          rpart_4.1-15        tidyselect_0.2.5   
[79] xfun_0.8