## 3 Methodology
### Shapley Additive exPlanation (SHAP)-Based FSS Method  
Shapley Additive exPlanation (SHAP) is one of the additive feature attribution values methods initially proposed by [PERSON] and [PERSON] (2017) and was designed for explainable AI (XAI) [8]. The explanation level is focused on comprehending how a model makes decisions based on its features and from each learned component. SHAP is a class of additive feature attribution methods that are model-agnostic and can be applied to any machine learning and deep learning model by attributing the importance of each input feature. In comparison to other additive feature attribution methods, such as LIM [25] and DeepLIFT [26], SHAP has a unique approach that satisfies the accuracy, missingness, and consistency properties of feature attribution. In SHAP, feature importance can be computed using ideas from game theory concepts. The model explanation can be computed at global and local levels. The model's global explanation assists in better understanding which features are important, as well as the interactions between different features. It is also more aligned with human intuition and is more effective at mining influential features. Hence, this paper introduces SHAP-values-assisted feature selection to identify relevant features with respect to the specified target variables in the context of a data center. The SHAP-assisted feature selection procedures used in this paper are depicted in Figure 1. The procedures were: (i) data collection and preprocessing; (ii) training the models using all features in the initial interaction; (iii) applying SHAP, computing the Shapley values of each feature, and ranking them in ascending priority order; (iv) training the models \(n\) times, beginning with the topmost features and continuing until the optimal subset is found with respect to each of the aforementioned methods; and (v) selecting the optimal feature subset to effectively model the target problem with the most predictable feature subset to optimize DC operations. In general, Shapley values can be computed as a unified measure of feature importance, which is the average of the marginal contributions of features from all conceivable coalitions. For example, we can compute the Shapley value of a given feature, \(n\), in each dataset, D. The value of the feature is replaced by a value from another instance of the model, and all possible outcomes are considered to compare the original prediction with the new prediction. Hence, the average between the new value and the original value represents the importance of feature \(n\) to the final prediction. For example, the Shapley value estimation of the \(j\)th feature with \(i\) combinations of features, target feature \(x\), \(j\) index, data streams \(D\) with matrix \(X\), and predictive model \(f\), Shapley value for \(x\) is computed as follows:  
\[\phi_{ij}=f^{{}^{\prime}}(x+j)-f^{{}^{\prime}}(x-j) \tag{1}\]  
where \(\phi_{j}^{i}\) is the average Shapley value of the \(j\)th feature with the \(i\)th feature, \(f^{{}^{\prime}}(x_{+j})\) is the prediction for target \(x\) with a random number of feature values, including \(j\)th feature, and \(f^{{}^{\prime}}(x_{-j})\) is the coalition without the \(j\)th feature. In general, to compute the Shapley value of the \(j\)th feature that is target \(x\), the equation is given as follows:  
\[\phi_{j}(x)=\frac{1}{n}\sum_{i=1}^{n}(\phi_{j}^{i}) \tag{2}\]  
The importance of all features is computed in the same way and is ranked based on their Shapley value in a prior order. As shown in the following iterations, the model is then trained using the most important features, beginning from the top and continuing until the optimal feature subset is found. 1. 1 st interaction: \(i_{1}=f_{1}\)
2. 2 nd interaction: \(i_{2}=f_{1},f_{2}\)
3. \(n\)th interaction: \(i_{n}=f_{1},f_{2},f_{3},\ldots\)\(f_{n}\)  
Finally, the optimal feature subset can be found and used to effectively model the target problem. The following Figure 1 shows the overall conceptual framework of the process.