# Prediction of Flotation Deinking Performance: A Comparative Analysis of Machine Learning Techniques
## 3 Results
It is further combined with ARD to determine the feature importance, as shown in Figure 4. The length scale is the parameter that estimates the relevance of the input features to predict the model's response. A small length scale indicates a highly relevant feature and vice versa. The surfactant concentration for both surfactants is the most important feature, whereas the flotation time has the smallest impact on the overall model performance. Figure 2: Optimization of the hyperparameters minimum leaf size and number of trees in random forests for estimating cellulose fiber recovery in the sink product (E\({}_{\text{m}}\)) when the surfactant is (**a**) oleic acid and (**b**) oleic acid + CaCl\({}_{2}\). Tables 3 and 4 present the prediction results of the flotation deinking performance using various machine learning techniques. The fiber recovery in sink product (E\({}_{\text{m}}\)) and the toner recovery in foam product (E\({}_{\text{t}}\)) were used to estimate the performance of flotation deinking in Tables 3 and 4, respectively. Oleic acid and oleic acid with addition of CaCl\({}_{2}\) were used as the surfactants in both cases. Figure 4: Feature selection using ARD in GPR for estimating cellulose fiber recovery in the sink product (Em) when the surfactant is (**a**) oleic acid and (**b**) oleic acid + CaCl\({}_{2}\). Figure 3: Optimization of the hyperparameters learning rate and number of trees in boosting for estimating cellulose fiber recovery in the sink product (E\({}_{\text{m}}\)) when the surfactant is (**a**) oleic acid and (**b**) oleic acid + CaCl\({}_{2}\). The prediction results for E\({}_{\text{m}}\) in Table 3 show that GPR with all covariance functions outperforms all other techniques by a large margin using both MSE and \(R^{2}\) as performance measures for prediction. The best overall result for \(R^{2}\) is obtained using the Matern 5/2 covariance function when oleic acid was used as the surfactant (\(R^{2}\) = 97.77%), whereas the Matern 3/2 covariance function yields the best performance when CaCl\({}_{2}\) was added to oleic acid (\(R^{2}\) = 95.95%). On the other hand, the squared exponential covariance function gives the best estimation for both surfactants when MSE was used as the performance measure. Boosting and SVR with the RBF kernel have comparable performances, which is 2-4% lower than GPR (measured by \(R^{2}\)), while the performance of SVR with the linear kernel is significantly worse, due to highly nonlinear dependencies between input data. Based on the presented results, it is shown that GPR using the squared exponential covariance function gave the best performance in the assessment of fiber recovery in the sink product considering MSE as the performance measure. The prediction results for E\({}_{\text{t}}\) presented in Table 4 are, in general, lower than for E\({}_{\text{m}}\). However, boosting outperforms all other machine learning techniques significantly for both performance measures, which is especially evident when oleic acid with the addition of CaCl\({}_{2}\) was used as the surfactant, where the second-best results were 15% lower, measured by \(R^{2}\). The dataset is limited (only 100 observations) and it is obviously not enough to capture the complex dependencies between the input features. However, boosting proved to be especially robust to our small-sample problem. The reason might be that boosting, as an ensemble method, can decrease the variance of a single estimate by combining more estimates from different models. Moreover, boosting, unlike random forests, can also reduce the bias by focusing on a weak single model and trying to decrease the prediction error in the next iteration, resulting in a model with higher stability.