Last updated: 2019-08-14
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Knit directory: polymeRID/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| 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 |
| Rmd | 5d28ce0 | goergen95 | 2019-08-14 | changed citation note |
| html | 5d28ce0 | goergen95 | 2019-08-14 | changed citation note |
| Rmd | c0c64ae | goergen95 | 2019-08-14 | proceed of rf_exploration |
| html | c0c64ae | goergen95 | 2019-08-14 | proceed of rf_exploration |
| Rmd | 90bd244 | goergen95 | 2019-08-14 | forward on rf_exploration |
| html | 90bd244 | goergen95 | 2019-08-14 | forward on rf_exploration |
| Rmd | c3f088e | goergen95 | 2019-08-13 | started exploration tab |
| html | c3f088e | goergen95 | 2019-08-13 | started exploration tab |
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 higher importance here. Different levels of data reprocessing 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 user defined 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 Savitkiy-Golay filter (Savitzky and Golay 1964) and first and second derivative of a raw spectrum. The functions 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 bear 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);Fu2014]. Simultaniously, 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.
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 effectivly 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 realise that this new dataset is not fit to be used in a training process. If we now randomly split the observations into training and test, we effectivly 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 beforhand 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 truely independent from the training process. Here, 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 refering to "training" and "testing".
head(pcaData[["repeat5"]][["fold10"]][["training"]]) PC1 PC2 PC3 PC4 PC5 PC6
1 -0.4779164 -0.7786770 -0.02761266 -0.06607284 -0.1414115 -0.1534971
2 -0.4869471 -0.7181236 -0.02492981 -0.05903759 -0.1850104 -0.1409379
4 -0.4661699 -0.7463479 -0.11424932 -0.03956596 -0.1056265 -0.1399688
6 -0.5257137 -0.5042399 0.10500327 -0.05850722 -0.2114660 -0.1380447
8 -0.5117566 -0.5967677 0.04001548 -0.04896668 -0.2129714 -0.1515174
11 -0.5237685 -0.5894120 0.05200442 -0.05865827 -0.2263991 -0.1561229
PC7 PC8 PC9 PC10 PC11 PC12
1 0.2060466 -0.04470884 0.1514982 -0.04843538 0.21485350 -0.011536533
2 0.1918080 -0.04751573 0.1395856 -0.03745341 0.17256791 -0.002443176
4 0.1775101 -0.05680964 0.1531349 -0.04319456 0.21718253 -0.003368534
6 0.1901325 -0.03195793 0.1066313 -0.02132166 0.09589942 -0.006065318
8 0.2032426 -0.03895545 0.1157844 -0.03040473 0.13270558 -0.002097848
11 0.2032640 -0.04166006 0.1209914 -0.02936654 0.12332775 -0.002840695
PC13 response
1 0.04706193 FUR
2 0.01465483 FUR
4 0.02593991 FUR
6 0.03218995 FUR
8 0.02925628 FUR
11 0.03068548 FURtail(pcaData[["repeat5"]][["fold10"]][["validation"]]) PC1 PC2 PC3 PC4 PC5 PC6
138 -0.6244338 -0.2251354 -0.04125220 -0.07484999 -0.27266002 -0.026217908
139 -0.5832934 -0.5663093 -0.39824689 -0.09269745 -0.06750005 0.007607282
142 1.3643143 -0.4874876 -0.04759479 1.69655907 0.26013483 0.009538671
143 0.9617909 -0.4624777 -0.07106849 1.24167453 0.20000959 0.002779168
144 -0.8842106 1.0703276 -0.77433375 -0.02590177 0.34894910 0.001737278
147 -0.6888015 0.1002989 0.40046959 -0.12243199 -0.48345619 0.076636770
PC7 PC8 PC9 PC10 PC11
138 0.06659313 0.002040475 -0.017318487 0.025721276 -0.16978522
139 0.03009946 -0.013417290 -0.056429051 0.006177153 -0.11445905
142 -0.20273071 0.178143838 0.486645669 0.618606076 0.13437431
143 -0.17007004 0.168194290 0.401200526 0.556734081 0.07242852
144 0.01314587 -0.029058498 0.223687515 -0.056605387 0.01770163
147 -0.14184110 -0.032212557 0.002410302 -0.007140975 -0.16104385
PC12 PC13 response
138 -0.0006882923 -0.050474176 PA
139 0.0199881958 -0.003416057 PA
142 -0.2862799869 -0.260510805 PUR
143 -0.2309708768 -0.247415734 PUR
144 0.0369931976 0.014124356 HDPE
147 0.0171552493 -0.050210341 PSsummary(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"]]$response)FIBRE FUR HDPE LDPE PA PE PES PET PP PS PUR WOOD
13 11 5 5 7 4 7 4 6 3 3 2 This process of splitting the dataset into training and test was automised by putting the above code in a function which can be found here. Finally, we can apply this function to the different levels of preprocssing which were discussed before.
source("code/functions.R")
wavenumbers = readRDS(paste0(ref,"wavenumbers.rds"))
# add noise to data
noisyData = addNoise(data,levels = c(0,10,100,250,500), category = "class")
# preprocessing
testDataset = createTrainingSet(noisyData, category = "class",
SGpara = list(p=3, w=11), lag=15,
type = c("raw", "norm", "sg", "sg.d1", "sg.d2",
"sg.norm", "sg.norm.d1", "sg.norm.d2",
"raw.d1", "raw.d2", "norm.d1", "norm.d2"))
types = names(testDataset[[1]])
levels = lapply(names(testDataset), function(x){
rep(x, length(types))
})
levels = unlist(levels)
results = data.frame(level=levels,type = types, kappa = rep(0,length(levels)))
for (level in unique(levels)){
for (type in types){
print(paste0("Level: ",level," Type: ",type))
tmpData = testDataset[[level]][[type]]
tmpData[which(wavenumbers<=2420 & wavenumbers>=2200)] = 0 # setting C02 window to 0
tmpModel = pcaCV(tmpData, folds = 10, repeats = 5, threshold = 99, metric = "Kappa", p=0.5, method="rf")
saveRDS(tmpModel,file = paste0(output,"rf/model_",level,"_",type,"_",round(tmpModel[[1]],2),".rds"))
results[which(results$level==level & results$type==type),"kappa"] = as.numeric(tmpModel[[1]])
print(results)
}
}
saveRDS(paste0(output,"rf/exploration.rds"))We can now take a look at the kappa scores the algorithm achived during training for different representations of the data and at increasing noise levels.
We can observe that with higher noise ratios the kappa score is reduced significantly. However, there are some data transformations which are able to maintain a relativly high level of accuracy even in the presence of noise. One of the best might be the simple Savitzkiy-Golay filter, as well as the same filter applied to the normalised data. Equal robust results are observed for the raw and the normalised data. The other transformations do not show the same level of robustness to noise. We can look at this more mathmatically by calculating the average slopes of the data tranformations methods and order the data frame from low to high slopes. Note that we only take the kappa score at noise level 0 and 500 to calculate the average slope.noise0 = results[results$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 normalised data followed by the raw and the normalised 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] colorspace_1.4-1 recipes_0.1.6 httpuv_1.5.1
[25] htmltools_0.3.6 Matrix_1.2-17 plyr_1.8.4
[28] timeDate_3043.102 pkgconfig_2.0.2 SparseM_1.77
[31] caret_6.0-84 xtable_1.8-4 purrr_0.3.2
[34] scales_1.0.0 whisker_0.3-2 later_0.8.0
[37] gower_0.2.1 lava_1.6.5 git2r_0.26.1
[40] tibble_2.1.3 generics_0.0.2 withr_2.1.2
[43] nnet_7.3-12 lazyeval_0.2.2 mime_0.7
[46] survival_2.44-1.1 crayon_1.3.4 evaluate_0.14
[49] fs_1.3.1 nlme_3.1-140 MASS_7.3-51.4
[52] class_7.3-15 tools_3.6.1 data.table_1.12.2
[55] munsell_0.5.0 zip_2.0.3 compiler_3.6.1
[58] rlang_0.4.0 grid_3.6.1 iterators_1.0.12
[61] htmlwidgets_1.3 crosstalk_1.0.0 labeling_0.3
[64] base64enc_0.1-3 rmarkdown_1.14 gtable_0.3.0
[67] ModelMetrics_1.2.2 codetools_0.2-16 R6_2.4.0
[70] tfruns_1.4 lubridate_1.7.4 zeallot_0.1.0
[73] rprojroot_1.3-2 stringi_1.4.3 Rcpp_1.0.2
[76] rpart_4.1-15 tidyselect_0.2.5 xfun_0.8