## 2 Materials and Methods
### Classification Model  
For the first time, this study used machine learning techniques to automatically individualize and classify the petrol sources of native, evaporated, and fire debris samples. They were implemented in MATLAB (R2019b) using the Classification Learner app. The evaluation of the model was performed using selected datasets, which are essential in experimental model development.  
The classification model research design is outlined as follows:  
Step 1--data collection. The datasets evaluated in this research were as follows:  
(1) entire \({}^{1}\)H NMR spectrum of neat petrol samples; (2) \({}^{1}\)H seITOCSY spectrum of the four olefins of neat petrol samples; (3) \({}^{1}\)H seITOCSY spectrum of the four olefins of neat and evaporated petrol samples; (4) \({}^{1}\)H seITOCSY spectrum of the four olefins of neat, evaporated, and fire debris residue samples.  
The datasets were divided into (i) training data, comprising non-targeting (contained all the NMR spectrum information) and targeting (\({}^{1}\)H seITOCSY spectrum that consisted of selected features that were recognized as an important feature for discrimination purposes) datasets and (ii) a blind study testing dataset (for the practical validation of the model by comparing to a real-world dataset). The training and testing datasets were used to determine the best classifier model for the classification of petrol brands based on the NMR spectrum.  
Step 2--reduction of data dimensionality by selecting only a subset of measured features (predictor variables) to create a cluster model through PCA or for the feature selection function (using the featured chemical bins from the PLS-DA VIP scores). The PCA function was enabled with a component reduction criterion of 80% of the explained variance as this represents a sufficient information variance; typically, the first few PCs correspond to cumulative eigenvalues accounting for 80% or above of the variation within a dataset and are sufficient to describe or explain most of the variability in the given dataset, thus reducing the dimensionality [3]. For optimal results, the study aimed to choose a classifier model with a minimum of 60% accuracy (validation).  
Step 3--dataset optimization. The effect of the pre-processed parameters on the classification training model for the discrimination of petrol samples was tested. Two different parameter pre-processing methods were investigated in this study: filtering of the redundant spectral bins and the normalization parameter. Data filtering was applied to set any spectral bin value less than 1 to 0. For normalization, (i) single peaks were normalized (to the highest peak of the spectrum) and (ii) normalized with the total area sum (LOG function).  
Step 4--dataset splitting. The datasets were split into training and testing datasets using the cross-validation function with K-folds. The cross-validation method with 5 and 10 folds was investigated.  
Step 5--evaluating different classifier models such as Decision Trees, Discriminant Analysis (DA), Support Vector Machines (SVMs), Logistic Regression, k-Nearest Neighbor (k-NN), Naive Bayes, Ensembles, and Artificial Neural Networks (ANNs).  
Step 6--after training multiple models, their performances were compared, and then the most robust and effective classification model was chosen. The Classification Learner app displayed the results of the validated model. Performance measures, such as model accuracy, and visual representation plots, such as the confusion matrix chart, reflect the validated model results. The confusion matrix table displayed six petrol brands as true classes in the rows and predicted classes in the columns.  
The goal of the classification model method was to investigate different datasets of native, evaporated and fire debris petrol samples with different pre-treatment techniquesincluding data filtering and normalization to identify the most desirable classifier which provides the highest classification accuracy.