## 3 Software and Image Processing
### Multivariate Statistical Analyses
#### 3.1.2 Supervised Methods  
Supervised classification and regression techniques (Table 2) can be used according to the specific application to predict qualitative or quantitative features by finding a relationship between a set of independent variables (optical outputs) that describes the objects (predictors) studied and a set of measured responses for the same objects [23; 24].  
Multivariate classification methods define the existing relation between the experimental variables (X matrix, the hypercube) and a qualitative variable that identifies the belonging class (y vector, response variable). Many methods like linear discriminant analysis (LDA), k-nearest neighbor (KNN), soft independent modeling of class analogy (SIMCA), support vector machine (SVM), and partial least square regression-discriminant analysis (PLS-DA) are used to define the membership of each sample to its appropriate class [25].  
Multivariate regression methods calculate the mathematical model for the relation between the X matrix and the y vector of the quantitative response [26]. The regression model design using HSI data is different from developing a traditional spectroscopic model, where each spectrum (Xi) has a corresponding measured variable (yi). Indeed, in hyperspectral images, there can be found thousands of spectra for the same measured variable, and a spectrum that represents the sample is calculated. The mean spectra for each sample are combined to create the data set (X), which is used with regression techniques to predict the corresponding observed values (y) [27]. For these purposes, methods like multiple linear regression (MLR), principal component regression (PCR), partial least square regression (PLSR), support vector machine regression (SVR), or artificial neural networks (ANNs) are broadly used [28].  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Method 1**} & \multicolumn{2}{c}{**Reference**} \\ \hline \multirow{4}{*}{**Classification**} & PLS-DA & [PERSON] et al. [29], [PERSON] et al. [30], [PERSON] et al. [31], [PERSON] et al. [32], [PERSON] et al. [33], [PERSON] et al. [34] \\ \cline{2-3}  & LDA & [PERSON] et al. [35], [PERSON] et al. [36] \\ \cline{2-3}  & KNN & [PERSON] et al. [31], [PERSON] et al. [32], \\ \cline{2-3}  & SIMCA & [PERSON] et al. [32], [PERSON] et al. [37] \\ \cline{2-3}  & SVM & [PERSON] et al. [38], [PERSON] et al. [33], [PERSON] et al. [39] \\ \hline \multirow{4}{*}{**Regression**} & PCR & [PERSON] et al. [40], [PERSON] et al. [41] \\ \cline{2-3}  & & [PERSON] et al. [31], [PERSON] et al. [40], [PERSON] et al. [42], [PERSON] et al. [43], [PERSON] et al. [44], [PERSON] et al. [45], [PERSON] et al. [46], [PERSON] et al. [47], [PERSON] et al. [48], [PERSON] et al. [49], [PERSON] et al. [34], [PERSON] et al. [50], [PERSON] et al. [51], [PERSON] et al. [52], [PERSON] et al. [53], [PERSON] et al. [54], [PERSON] et al. [41] \\ \cline{2-3}  & MLR & [PERSON] and [PERSON] [55], [PERSON] and [PERSON] [56], [PERSON] et al. [57], [PERSON] et al. [45] \\ \cline{2-3}  & ANNs & [PERSON] et al. [58], [PERSON] et al. [53] \\ \cline{2-3}  & SVR & [PERSON] et al. [59], [PERSON] et al. [60], [PERSON] et al. [61] \\ \cline{2-3}  & LS-SVM & [PERSON] et al. [45], [PERSON] et al. [49] \\ \hline \hline \end{tabular}  
* PLS-DA = partial least square–discriminant analysis; LDA = linear discriminant analysis; KNN = k-nearest neighbor; SIMCA = soft independent modeling of class analogy; SVM = support vector machine; PCR= principal component regression; PLSR = partial least square regression; MLR = multiple linear regression; ANNs = artificial neural networks; SVR = support vector regression; LS-SVM = least square support vector machine.  
\end{table}
Table 2: Overview of the classification and regression algorithms used for fresh-cut fruit and vegetable analysis.