*2.6. Estimating the Muscle Texture Indicators with the Skin HSI Data*

With the processed skin HSI data in each region, we used six machine learning (ML) methods to estimate the texture indicators of the muscle in the corresponding region. The methods included partial least-square regression (PLSR), the interval partial leastsquare method (iPLS), the synergy interval partial least-square method (SiPLS), backward interval partial least squares (BiPLS), least-square support vector machines (LS-SVM), and backpropagation artificial neural network (BP-ANN).

PLSR projects the predictor variables and observable variables into a new feature space to build a linear regression model [33]. PLSR decomposes the independent variable X and the dependent variable Y into several X-scores (T) and constructs the PLSR model. Herein, the observed variables were the cross-validation performed to minimize the error between the predicted and the observed response values.

In the iPLS algorithm, the full spectral region is divided into smaller equidistant subintervals, and a PLS regression model is generated based on each subinterval. The best intervals and principal component scores are selected based on the principle of the lowest root-mean-square error for the calibration (RMSEC) value [34].

The SiPLS algorithm is a modified iPLS where the full spectral region is divided equally into subintervals. The combination with the lowest RMSEC value is selected [34].

The BiPLS algorithm divides the whole spectral region into N subintervals of equal width and performs PLS regression, each interval is omitted in turn, and the worst RMSEC value is obtained in the modeling; the subintervals continue to be removed until the lowest RMSEC value is obtained [34].

LS-SVM uses the radial basis kernel function (RBF), a non-linear function that reduces the complexity of the training process [35]. The regularization parameter gamma (γ) and the kernel parameter (σ2), which can reduce the complexity, represent the width of the RBF kernel. To achieve high prediction accuracy, we performed the simulations of these two parameters, the values of which ranged from 0 to 1000 [6].

In BP-ANN models, an error-reversal propagation algorithm is used to train multilayer feedforward neural networks [36]. A BP-ANN, with an input layer, a hidden layer, and an output layer was established. Moreover, the transfer function, learning function, and training function were employed. The maximum training step was set to 1000, the learning goal was e<sup>−</sup>5, and the learning rate and momentum factor were 0.01.

#### *2.7. Evaluating the Accuracies of Six ML Models*

The predictive accuracy of each ML model was assessed with multiple parameters, including coefficients of determination for calibration (*r*C) and prediction (*r*P), RMSEC, and the root-mean-square error for calibration and prediction (RMSEP) [37]. The *r*<sup>C</sup> and *r*<sup>P</sup> values were calculated as follows:

$$r\_{\mathbb{C}} = \sqrt{\frac{\frac{\sum\_{i=1}^{n\_c} \left(\hat{y}\_i - y\_i\right)^2}{\sum\_{i=1}^{n\_c} \left(\hat{y}\_i - y\_c\right)^2}}{\sqrt{\frac{\sum\_{i=1}^{n\_p} \left(\hat{y}\_i - y\_i\right)^2}{\sum\_{i=1}^{n\_p} \left(\hat{y}\_i - y\_p\right)^2}}}}}$$

where *<sup>y</sup>*ˆ*i* and *yi* represent the predicted and measured TPA values, respectively; *nc* and *np* represent the number of samples in the calibration and prediction sets, respectively.

The RMSEC and RMSEP were calculated as follows:

$$\text{RMSE} = \sqrt{\frac{1}{N - 1 - R} \times \sum\_{i=1}^{N} \left( y\_i^{ref} - y\_i \right)^2}$$

where *N* is the number of samples, *R* is the number of factors of the model, *yref i* is the reference value of the sample, and *<sup>i</sup>* and *yi* are the predicted values of the sample.

$$\mathbf{RMSE} = \sqrt{\frac{\mathbf{1}}{N} \times \sum\_{i=1}^{N} \left( y\_i^{ref} - y\_i \right)^2}$$

Herein, for each texture indicator, *yref i* was the observed value in the common carp muscle, while *yi* was the predicted value with one ML method and the reflectance values of corresponding skin HSI. The lower RMSEC and RMSEP values indicated a smaller difference between the predicted texture indicator and the observed indicator. A good ML model was expected to have high *r*<sup>C</sup> and *r*<sup>P</sup> but low RMSEC and RMSEP values [38].
