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Knit directory: polymeRID/
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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.
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 0.002650597Then, 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 0.02503375The 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.
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$response = responseVal
foldtmp = list(training, validation)
names(foldtmp) = c("training","validation")
return(foldtmp)
})
names(pcadata_fold) = paste("fold", 1:folds, sep ="")
pcaData[[paste0("repeat",rep)]] = pcadata_fold
}We now have a list object with the number of elements equivalent to the repeats. Below each repeat element we can access the individual folds. There we find two elements which we can access by referring to "training" and "testing".
pcaData[["repeat5"]][["fold10"]][["training"]][1:3,1:3] PC1 PC2 PC3
1 -0.4779164 -0.7786770 -0.02761266
2 -0.4869471 -0.7181236 -0.02492981
4 -0.4661699 -0.7463479 -0.11424932pcaData[["repeat5"]][["fold10"]][["validation"]][1:3,1:3] PC1 PC2 PC3
3 -0.5240744 -0.5931111 0.05961383
5 -0.4718366 -0.6995376 -0.09273887
7 -0.5255215 -0.5928214 0.05184969summary(pcaData[["repeat5"]][["fold10"]][["training"]]$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"]]$response)FIBRE FUR HDPE LDPE PA PE PES PET PP PS PUR WOOD
13 11 5 5 7 4 7 4 6 3 3 2 For the RF algorithm only the parameter mtry needs a search pattern since we hold the number of trees constant at a value of 500. mtry effectively specifies the number of variables to look at each split within a tree. We took the square root of the number of variables divided by 3 as the first mtry value, the square root itself as the second and the maximum number of variables as a third value. The optimal parameter is then selected to build the final model and it is evaluated with the test data.
training = pcaData[["repeat1"]][["fold1"]][["training"]]
validation =pcaData[["repeat1"]][["fold1"]][["validation"]]
x_train = training[ ,1:ncol(training)-1]
y_train = training$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$table) Reference
Prediction FIBRE FUR HDPE LDPE PA PE PES PET PP PS PUR WOOD
FIBRE 8 0 0 0 0 0 0 0 0 0 0 1
FUR 2 11 0 0 0 0 0 0 0 0 0 0
HDPE 0 0 3 0 0 0 0 0 0 0 0 0
LDPE 0 0 0 5 0 0 0 0 0 0 0 0
PA 0 0 0 0 7 0 0 0 0 0 0 0
PE 0 0 1 0 0 4 0 0 0 0 0 0
PES 0 0 0 0 0 0 6 0 0 0 0 0
PET 0 0 1 0 0 0 1 4 0 0 0 0
PP 0 0 0 0 0 0 0 0 6 0 0 0
PS 0 0 0 0 0 0 0 0 0 3 0 0
PUR 0 0 0 0 0 0 0 0 0 0 3 0
WOOD 3 0 0 0 0 0 0 0 0 0 0 1This process of splitting the data set into training and test was automated by putting the above code in a function which can be found here. Finally, we can apply this function to the different levels of prepossessing which were discussed before.
source("code/functions.R")
wavenumbers = readRDS(paste0(ref,"wavenumbers.rds"))
# add noise to data
noisyData = addNoise(data,levels = c(0,10,100,250,500), category = "class")
# preprocessing
testDataset = createTrainingSet(noisyData, category = "class",
SGpara = list(p=3, w=11), lag=15,
type = c("raw", "norm", "sg", "sg.d1", "sg.d2",
"sg.norm", "sg.norm.d1", "sg.norm.d2",
"raw.d1", "raw.d2", "norm.d1", "norm.d2"))
types = names(testDataset[[1]])
levels = lapply(names(testDataset), function(x){
rep(x, length(types))
})
levels = unlist(levels)
results = data.frame(level=levels,type = types, kappa = rep(0,length(levels)))
for (level in unique(levels)){
for (type in types){
print(paste0("Level: ",level," Type: ",type))
tmpData = testDataset[[level]][[type]]
tmpData[which(wavenumbers<=2420 & wavenumbers>=2200)] = 0 # setting C02 window to 0
tmpModel = pcaCV(tmpData, folds = 10, repeats = 5, threshold = 99, metric = "Kappa", p=0.5, method="rf")
saveRDS(tmpModel,file = paste0(output,"rf/model_",level,"_",type,"_",round(tmpModel[[1]],2),".rds"))
results[which(results$level==level & results$type==type),"kappa"] = as.numeric(tmpModel[[1]])
print(results)
}
}
saveRDS(paste0(output,"rf/exploration.rds"))We can now take a look at the kappa scores the algorithm achieved during training for different representations of the data at increasing noise levels.
We can observe that with higher noise ratios the kappa score is reduced significantly. However, there are some data transformations which are able to maintain a relatively high level of accuracy even in the presence of noise. One of the best might be the simple Savitzkiy-Golay filter, as well as the same filter applied to the normalized data. Equal robust results are observed for the raw and the normalized data. The other transformations do not show the same level of robustness to noise. We can look at this more mathematically by calculating the average slopes of the data transformations methods and order the data frame from low to high slopes. Note that we only take the kappa score at noise level 0 and 500 to calculate the average slope.noise0 = results[results$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.
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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