## 2 Materials and Methods
### Data Processing  
Based on [PERSON] et al. (2019), the detection of _G. boninense_ was determined by analyzing specific spectral signatures of U and I treatments. Only the bands that attained the highest separation between treatments and statistically significant were included for further processing to avoid analytical issues due to unnecessary data. Initially, 35 bands were chosen based on the work of [PERSON] et al. (2019). Then the number of bands was optimized based on the performance of machine learning classification models. The models were developed using seven machine learning algorithms available in MATLAB's machine learning toolbox (2019b, The MathWorks Inc., Natick, MA, USA), ran on a personal computer equipped with an Intel(r) Core(tm) i7-8750H processor and 32 GB RAM. Each algorithm is generally described as below:  
1. Decision trees build classification in the form of a tree structure. The classifier breaks down a dataset into smaller and smaller subsets while at the same time an associated decision tree is incrementally developed. The final result is a tree with decision nodes and leaf nodes. The leaf nodes contain responses in nominal terms such as 'true' or 'false'. 2. Discriminant analysis assumes that different classes generate data based on different Gaussian distributions. For example, LDA model has the same covariance matrix for each class with different means, while QDA has both covariances and means of each class different. LDA (Equation (2)) and QDA (Equation (3)) can be expressed as: \[\beta=C^{-1}(\mu_{1}-\mu_{2})\] (2) where \(\beta\) is the linear model coefficients, \(C\) is the covariance matrices, and \(\mu_{i}\) are the mean vectors. \[Z_{k}(x)=-\frac{1}{2}(x-\mu_{k})^{T}C_{k}^{-1}(x-\mu_{k})-\frac{1}{2}ln|C_{k} |+lnP(C_{k}).\] (3) where \(C_{k}\) is the covariance matrix for the class \(k^{-1}\), \(|C_{k}|\) is the determinant of the covariance matrix \(C_{k}\), and \(P(C_{k})\) is the prior probability of the class \(k\). 3. Logistic regression predicts the probability of an outcome that can only have two values. The prediction is based on the use of one or several predictors (numerical and categorical). Equation of logistic regression is as below: \[l=\log_{b}\frac{p}{1-p}=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}\] (4)  
Figure 2: Spectral extraction using Cube-Pilot of left and right leaflets. where \(p=P(Y=1)\), \(b\) is the base of logarithm, \(\beta_{i}\) are parameters of the model, and \(x_{i}\) are the predictors. 4. Naive Bayes is a type of probabilistic classifier that discriminates different objects based on specific features. Bayes theorem is represented as: \[P(A|B)=\frac{P(B|A)\ P(A)}{P(B)}\] (5) where \(A\) and \(B\) are events and \(P(B)\
eq 0\). \(P(A|B)\) and \(P(B|A)\) are conditional probabilities, and \(P(A)\) and \(P(B)\) are the probabilities of observing \(A\) and \(B\) independently of each other; this is known as the marginal probability. 5. Support Vector Machine (SVM) performs classification by finding the hyperplane that maximizes the margin between the two classes. The vectors (cases) that define the hyperplane are the support vectors. The linear kernel is fit for linearly separable data, which can be expressed as: \[k(x_{i},x_{j})=x_{i}^{T}x_{j}\] (6)
6. where \(k\) is the kernel function, \(\left(x_{i},x_{j}\right)\) are \(a\)-dimensional input \(x_{i}^{T}x_{j}\) is a map from \(a\)-dimension to \(b\)-dimension. An example of non-linear kernels is Gaussian Radial Basis Function (RBF), which can be represented as: \[ \begin{split} k\big{(}x_{i},x_{j}\big{)}=\exp\left(-\frac{\|x_{i}- x_{j}\|^{2}}{2\sigma^{2}}\right)\\ =\exp\left(-\gamma\|x_{i}-x_{j}\|^{2}\right)\end{split} \] (7) where \(\|x_{i}-x_{j}\|^{2}\) is known as the squared Euclidean distance between two feature vectors, and \(\sigma\) is defined as kernel width. Small kernel width tends to reflect dissimilar patterns and cause overfitting, whereas large ones result in very similar patterns and cause underfitting.