*3.6. Sequential Feature Selection Results*

We used backward sequential feature selection under a linear model and a decision tree regression (no linear model). However, implementation of the sequential feature selection through the decision tree may have generated overfitting; thus, a 10-fold cross-validation allowed the recognition of the accepted characteristics by modifying the tree depth from 2 to 5.

3.6.1. Sequential Feature Selection with Linear Regression Model

Table 7 presents the results obtained for the linear regression model (Section 2.8.1) determining the feature elimination sequence, which used as attributes the admitted range from 1 to 6. The table follows the logic of Figure 5, showing each color in the elimination ranking with the variance threshold.

**Table 7.** *Cont.*

3.6.2. Sequential Feature Selection with Decision Tree Regression Model

The feature recognition through the decision tree regression model used the variance in a specific feature, which ranged from 1 to 6, allowing the elimination order for each input variable (Tables 8–11) to be obtained from the tree depth configuration. A color image of each feature, following the structure for variance threshold selection, is shown in Figure 5.


**Table 8.** Sequential feature selection by decision tree for depth = 2.


**Table 9.** Sequential feature selection by decision tree for depth = 3.


**Table 10.** Sequential feature selection by decision tree for depth = 4.


**Table 11.** Sequential feature selection by decision tree for depth = 5.

#### **4. Discussion**

The results obtained require division into linear and nonlinear model selection algorithms. The division generated makes it possible to analyze the results according to the model type and to identify the sequence of each feature. Tables 12 and 13 show the algorithms by group, the feature selection order, and the mean.



**Table 13.** Elimination order for the nonlinear model group.


The averages calculated and reported in Tables 12 and 13 indicate two different behaviors depending on the model performance (linear or nonlinear). Figure 8 shows an alternative way to visualize the performance between linear and nonlinear models.

**Figure 8.** Feature elimination order distributions with algorithms from the two models used.

After dividing the models into linear and nonlinear groups, we validated the ordinal elimination variables on a scale from 1 to 7 and tested the distributions with the Kruskal– Wallis test (Table 14) [61]. The sequence elimination distribution for the proposed models is shown in Figures 9 and 10 (linear and nonlinear models, respectively).

**Table 14.** Values obtained with the Kruskal–Wallis test.


**Figure 9.** Order of elimination for features in linear models.

The linear model indicated that the essential characteristic was intensity, while the least significant was the duty cycle (Figure 9 and Table 14). If the appropriate sequence for any variable is required, the mean value can be found in Table 12. This means that the elimination order for the linear models was duty cycle, G, R, W, B, frequency, and intensity.

The nonlinear model found that the most crucial characteristic was intensity, while the least important was W (white color), with sufficient significance *p* < 0.05. If the correct sequence of the other variables is required, we can rely on the mean values for the feature distribution (Table 13). Overall, the elimination sequence was W, G, B, duty cycle, frequency, R, and intensity.

The elimination order for the duty cycle and R in the linear and nonlinear models suggests that they are nonlinear features, mainly because several linear algorithms selected them as the first variables to eliminate but nonlinear algorithms selected them as the most important ones.

**Figure 10.** Order of elimination for features in nonlinear models.
