## 4 Results and Discussion
However, these methods suffer from a high frequency and cardinality of features in the relevant feature selection process, which may result in wrong conclusions. The SHAP-values-assisted FSS method introduced in this paper, on the other hand, outperformed the other methods for identifying relevant features in the context of a data center. According to the conceptual framework of the SHAP-assisted feature selection process presented in Section 3.3, it is model-agnostic and can be used with any machine learning model. In this paper, we used TreeSHAP with RF and XGB models to demonstrate FSS methods. Hence, Tables 2 and 3 demonstrate that the RFSVFIR and XGBSVFIR which are SHAP-values-assisted FSS methods outperformed other methods, demonstrating lower errors and fair speed. RFSVFIR performed with an MAE of 0.42, RMSE of 0.237, MAPE of 0.018, and an MAE of 1.368, RSME of 6.657, and MAPE of 0.005 at predicting the DC ambient temperature and DC energy demand target variables, respectively, with a fair computational speed. XGBSVFIR, on the other hand, predicted the DC ambient temperature and DC energy demand target variables with lower errors of a MAE of 0.401, RMSE of 0.245, MAPE of 0.0035, and a MAE of 0.451, RSME of 0.235, and MAPE of 0.004, respectively, with fair computational speed. When we compared XGBSVFIR with RFSVFIR, XGBSVFIR outperformed RFSVFIR, demonstrating a better performance and fair computational expenses. Hence, SHAP with XGB feature selection was faster when compared with SHAP with RF due to the capacity for parallel computation in XGB. Furthermore, due to its optimized hyperparameter with TreeSHAP [31]. Hence, as demonstrated by the experimental results in Tables 2 and 3, XGBSVFIR is the best-suited FSS method in the context of a data center for identifying the relevant operational features and underlying patterns to effectively model and optimize DC operations. To visualize the experimental results of the most suitable FSS method, we relied on three plots: SHAP feature importance, SHAP summary, and partial dependency plots. Hence, the graphs are based on the XGBSVFIR feature selection method. SHAP feature importance plots visualize features based on their feature importance, which is prioritized with high, absolute Shapley values. The feature importance of each feature is computed as the average absolute Shapley value of each feature across the data streams, as below:  
\[\phi_{j}(x)=\frac{1}{n}\sum_{i=1}^{n}|\phi_{j}^{i}| \tag{6}\]  
Following the Shapley value results, we sorted the feature importance from highest to lowest and plotted the graph. Figures 2a and 3a illustrate the SHAP feature importance plots based on the XGBSVFIR method at predicting the data center ambient temperature (amb_temp) and energy demand (dcenergy) target variables, respectively. The y-axes represent the names of the features and x-axis represents the Shapley values. The Shapley values indicate how much each feature influences the prediction of the target variable. Although SHAP feature importance is useful for visualizing the importance of features, it does not provide further information, aside from the importance. SHAP summary plots can provide additional information about the effects of each feature on the target variable. The SHAP summary plot provides the dispersion information of Shapley per each feature. Figures 2b and 3b display SHAP summary plots of the features used to predict data center ambient temperature and energy demand, respectively. The y-axis displays feature names and Shapley values, while the vertical line represents the accumulated density. The feature effect is represented by two colors: red for the greatest influence and blue for the least influence. In general, the topmost features are the most predictable. Figure 3: (**a**) SHAP feature importance plot. (**b**) SHAP summary plot.