Last updated: 2019-08-19

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Knit directory: polymeRID/

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File Version Author Date Message
Rmd d960dc2 goergen95 2019-08-19 included calibration

Overview

For the calibration we implemented a decision fusion between the best performing models in the exploration stage. Since SVM-based models did not achieve very high accuracies we only included two RF models and two CNN. The RF models yielding to the highest accuracies were trained with with the raw data and the Savitzkiy-Golay smoothed data. For the CNNs, we observed the highest accuracies with with the second derivative of the raw data and with the second derivative of the normalized data. These models are going to be used during calibration. To get an accuracy value for the fusion approach, again we use and cross-validation approach.

Cross Validation

The cross-validation of the decision fusion was conducted on 10 folds and repeated 5 times. The complete code can be found here. For every fold, 4 models are trained and evaluated against a 50% test split. The final decision is then achieved by combining the probability output of each model and assigning the class with the highest overall probability.

    classRFRaw = as.character(predict(rfModRaw, pcaRaw_testing))
    propRFRaw =  predict(rfModRaw, pcaRaw_testing, type = "prob")
    classRFSG = as.character(predict(rfModSG, pcaSG_testing))
    propRFSG = predict(rfModSG, pcaSG_testing, type = "prob")
    classCNND2 = as.character(classes[keras::predict_classes(cnnD2, x_testD2)+1])
    propCNND2 = keras::predict_proba(cnnD2, x_testD2)
    classCNNND2 = as.character(classes[keras::predict_classes(cnnND2, x_testND2)+1])
    propCNNND2 = keras::predict_proba(cnnND2, x_testND2)

    # probability
    probs = (propRFRaw + propRFSG + propCNND2 + propCNNND2) / 4
    pred = lapply(1:nrow(probs), function(x){
      which.max(probs[x,])
    })

    predVals = lapply(1:nrow(probs), function(x){
      probs[x,unlist(pred)[x]]
    })

    predVals = unlist(predVals)
    pred= names(unlist(pred))
    obsv = as.character(testingRaw$class)

    pred[which(pred %in% c("FIBRE","FUR","WOOD"))] = "OTHER"
    obsv[which(obsv %in% c("FIBRE","FUR","WOOD"))] = "OTHER"

    obsv = as.factor(obsv)
    pred = as.factor(pred)
    cfMat = caret::confusionMatrix(pred,obsv)

Note, that we combine the classes which are not synthetic polymers to a class called OTHER since we are only interested in the correct classification of plastic polymers. If a particle is correctly identified as non-plastic the main goal of the analysis is achieved, no matter if the different models disagree on exact non-plastic class. By using the caret::confusionMatrix() function we easily get overall accuracy values as well as class specific metrics.

Results

By calculating the average across all folds and all repeats we end up with our final accuracy results per class and in general.

Tab. 1: Overall accuracy values for the decision fusion after cross-validation.
value
Accuracy 0.914
Kappa 0.894
AccuracyLower 0.824
AccuracyUpper 0.966
AccuracyNull 0.371

We achieved an overall accuracy of 91.4% with a Kappa coefficient of 0.89 (Tab. 1). This is accuracy is substantially higher than compared to the single model accuracies of RF and CNN. By the decision fusion and combining the non-synthetic classes we were able to rise the accuracy about 5%.

Tab. 2: Class specific accuracy metrics for the decision fusion after cross-validation.
Sensitivity Specificity Pos Pred Value Neg Pred Value Precision Recall F1 Prevalence Detection Rate Detection Prevalence Balanced Accuracy
Class: HDPE 0.860 0.994 0.932 0.989 0.932 0.860 0.896 0.071 0.061 0.067 0.927
Class: LDPE 0.960 0.990 0.895 0.997 0.895 0.960 0.919 0.071 0.069 0.078 0.975
Class: OTHER 0.965 0.978 0.964 0.980 0.964 0.965 0.964 0.371 0.359 0.373 0.972
Class: PA 0.946 0.991 0.928 0.994 0.928 0.946 0.934 0.100 0.095 0.103 0.968
Class: PE 0.895 0.996 0.948 0.994 0.948 0.895 0.912 0.057 0.051 0.055 0.946
Class: PES 0.691 0.980 0.832 0.967 0.832 0.691 0.734 0.100 0.069 0.087 0.836
Class: PET 0.755 0.974 0.658 0.985 0.658 0.755 0.688 0.057 0.043 0.067 0.865
Class: PP 1.000 0.999 0.989 1.000 0.989 1.000 0.994 0.086 0.086 0.087 0.999
Class: PS 0.987 0.999 0.980 0.999 0.980 0.987 0.981 0.043 0.042 0.043 0.993
Class: PUR 0.920 0.999 0.978 0.997 0.978 0.920 0.960 0.043 0.039 0.041 0.959

When we analyse the class specific accuracy metrics (Tab. 2) we observe that the lowest sensitivity is 0.69 for PES. That means that PES is most likely to not be identified correctly. PET shows a similar low sensitivity value of 0.76. PP shows the highest sensitivity value of 1, which means that all samples classified as PP actually represent that class. Concerning the specificity, across all classes we observe similar values of about 0.99. In general, we can state that we achieved a very good distinction between non-synthetic polymers and microplastic polymers. However, some microplastic polymers, such as PES and PET achieve only poor accuracies (0.84 and 0.86 of balanced accuracy respectively). These shortcomings might be compensated for with future extensions of the training data base which could include more samples, especially for these two classes as well as others. In the end, the machine learning algorithms can only learn from the data base which is presented to them. Therefore, adding reference samples could prove beneficial when it comes to 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