## 2 A Theoretical Review of Feature Selection Methods  
In a given data stream, \(D\), with \(n\) features, \(2^{n}\) possible feature subsets can be generated. However, all these subsets may not be relevant for modeling and mining important patterns. Some features may appear to be equidistant, redundant, irrelevant, or noisy. To overcome these challenges, there are two special methods used to identify relevant features [9]. The first method is feature extraction/dimensional reduction, which transforms the original input feature into a reduced representation set. The second method is feature selection, which identifies relevant subsets while preserving the original information [10; 11]. Hence, in this paper, we focus on feature selection methods for identifying relevant features in the context of a data center. The main classes of feature selection (FS) methods are wrapper methods, embedded methods, and filter methods [12]. Wrapper methods use the model's performance as a score to select relevant feature subsets [13]. Although wrappers are effective methods, they are computationally expensive and in some case pros to overfitting [14]. On the other hand, embedded feature selection methods are applied during the model training process and are associated with a specific learning algorithm [11; 12]. Filter methods are another model-independent feature selection method that are typically applied in the preprocessing steps [15]. The best method, however, is usually determined depending on the problem identified. Data center operational management data streams are multivariate time series problems. The data streams are sequences of observations, denoted as \(x_{i}\) (\(t\)); [\(i=1\), \(n\); \(t=1\), \(\ldots\), \(T\)] [16], in which \(x\) represents observations, \(i\) represents measurements taken at each time point, \(t\), \(n\) is the maximum index, and the maximum time length is \(T\). The time series can be a univariate time series (UTS) problem or a multivariate time series (MTS) problem. It may be an MTS if the number of features, \(n\), is greater than or equal to 2, and it may be a UTS if n=1. This paper focuses on an MTS because the data center operations management data streams at hand are stored in a multi-dimensional matrix represented as \(m*n\), where \(n\) represents features in the data streams and \(m\) represents rows in the data streams. The target variables for the data center ambient temperature and data center energy demand are determined not only by their previous history but also by several other operational factors. The interaction between streams over time is the key to the complexity of the MTS problem. Thus, feature subset selection (FSS) entails identifying relevant features from given data streams with three main objectives. The objectives are: To provide insights into the data, reduce computational expense, and improve model performance [12]. To achieve these objectives, many studies have been conducted to identify relevant features in regression problems. For example, wrapper methods such as recursive feature elimination (RFE) and backward feature elimination (BFE) take input in the form of a single-column vector of the matrix. However, MTS data streams are stored in the form of a multidimensional matrix, which may lose important information during vectorization. Additionally, MTS data streams typically contain complex correlations between features over time that make it difficult to apply wrapper and embedded feature selection methods to MTS problems. Filter methods are correlation-based feature selection techniques that are effective on time series or continuous variables that compute correlations among different features and the target variable. Using correlation-based methods such as Pearson, Spearman, and Kendall, filter methods identify relevant features that have high correlations to the target variable. Filter methods identify relevant FSSs related to the target variable based on distance, dependency, and consistency [17].