## 2 Materials and Methods
### Data Analysis  
In this study, partial least-squares regression (PLSR) and support-vector regression (SVR) models were used to analyze the meat data. PLSR is the most frequently applied chemometric technique to predict the sample quality. It is an extension of the multiple linear regression model, which is widely \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample Type** & **Parameter** & **N** & **Range** & **Mean \(\pm\) SD** & **Skewness** & **Kurtosis** \\ \hline \multirow{3}{*}{Sirloin} & Fat & 50 & 7.54–37.47 & 21.32 \(\pm\) 6.51 & 0.08 & 2.64 \\  & Moisture & 50 & 47.52–73.86 & 59.09 \(\pm\) 6.35 & 0.15 & 2.25 \\  & Protein & 50 & 3.28–32.11 & 19.50 \(\pm\) 5.83 & \(-\)0.25 & 3.31 \\ \hline \multirow{3}{*}{Turkey} & Fat & 40 & 4.10–56.70 & 25.54 \(\pm\) 13.18 & 0.37 & 2.29 \\  & Moisture & 40 & 26.55–72.01 & 51.09 \(\pm\) 12.03 & \(-\)0.24 & 2.35 \\  & Protein & 40 & 7.44–28.49 & 18.07 \(\pm\) 4.97 & \(-\)0.20 & 2.43 \\ \hline \multirow{3}{*}{Tenderloin} & Fat & 50 & 7.60–22.33 & 16.85 \(\pm\) 4.01 & \(-\)0.75 & 2.30 \\  & Moisture & 50 & 57.78–70.55 & 63.75 \(\pm\) 3.14 & \(-\)0.15 & 2.42 \\ \cline{1-1}  & Protein & 50 & 7.50–23.06 & 16.88 \(\pm\) 4.19 & \(-\)0.61 & 2.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of measured parameters. used to specify the linear relationship between a dependent variable (\(\gamma\)-matrix) and independent variables (X-matrix) [12]. In this study, the independent variable was the spectral data obtained from the multispectral device, while the dependent variable was the chemical parameters (e.g., moisture, fat, and protein content) measured using conventional methods. The goal of the PLSR model is to predict the chemical parameters of the meat samples. In the PLSR model, data decomposed into orthogonal structures called latent variables (LVs). The LVs describe the maximum covariance between the spectral data and the response variables [25]. To build a regression model for predicting the chemical components in the meat, the entire dataset (X and Y matrix data) was divided into calibration and prediction sets using the Kenard-Stone (KS) algorithm. KS algorithm uniformly divides the samples by calculating the Euclidean distances between the X variables [26]. By using the KS method, 70% percent of the data were used to build the calibration dataset, while 30% were used as the prediction dataset. Further, the PLS model was constructed using the calibration set, while the prediction set was retained for testing the model's performance. However, to prevent the model from over-fitting or under-fitting, it was critical to select the optimal number of latent variables (LVs) for the regression model. The optimal number of LVs was selected using the lowest value from the root-mean-square error (RMSE) method during the cross-validation (leave-one-out) process. The equation is as follows:  
\[RMSE_{cv}=\sqrt{\frac{1}{n}\ \sum_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}}}, \tag{2}\]  
where \(\hat{y}_{i}\) and \(y_{i}\) are the predicted and measured chemical values, respectively, and n is the number of observations in the calibration set. Similar to PLSR, SVR also solves regression problems. However, its advantage over PLSR is that it solves both linear and non-linear problems using an optimization approach. SVR fits data into the linear regression model, y = wx + b, between the independent variable (x) and the dependent variables (y) by minimizing the cost function. The final SVR function can be expressed as:  
\[y(x)=\sum_{k=1}^{n}{\alpha_{k}K(x,x_{k})+b}, \tag{3}\]  
where \(\alpha_{k}\) are Lagrange multipliers, b is the bias term obtained from the optimization process, \(K(x,x_{k})\) is the kernel function, and \(x_{k}\) and \(x\) are the input training and testing vectors, respectively. A radial basis function (RBF) was used to develop the SVR model, while optimal kernel parameters (\(\gamma\) and C) were used to train the dataset.