## 3 CCD Assault Detection Using Euclidean Distance-Based Anomaly Detection Schemes
### Dimensionality Reduction Using Genetic Algorithm-Based Feature Selection  
The goal of FS is to choose a subset of features (from a given set of features) that yields minimum classification error. Works reported on dimensionality reduction affirm that FS techniques retain data characteristics for interpretability. Furthermore, overfitting due to fewer redundant data is reduced and modeling accuracy is improved with FS methods [29; 30; 31; 32; 33; 34]. The interrelationship between numerous dimensionality reduction approaches (encompassing feature subset selection) and FE with different flavors of PCA techniques was studied. [PERSON] et al. [30] analytically tested the effects of these methods on classification accuracy with two different types of datasets (email data and drug discovery data). The results revealed that feature transformation using PCA is highly sensitive to the type of data. Generally, FS methods can be divided into three categories: filters, wrappers, and embedded/hybrid methods. Wrapper methods are advantageous over filter approaches due to them giving better performance since they use the target classifiers such as K-nearest neighbors and support vector machine for feature selection. For a large dataset, however, wrapper methods are computationally expensive. The filter approach is known to be more computationally efficient than wrapper methods and performs well with large dataset [29; 35]. In this paper, considering the delay-sensitive nature and increasing sizes of power systems, we use a filter-based FS mechanism that is independent of any learning algorithm or classifier. Working as a preprocessor in the paper, the filter-based FS will select features by considering their scores in different statistical tests for correlation with the outcome variable. We use GA to select the subset of features from the SE-MF dataset that is the best at discriminating compromised data from normal data. GA has been widely used for FS purposes in the machine learning and is considered suitable for large combinatorial problems [30; 31; 36]. However, recently, particle swarm optimization (PSO) and other evolutionary and metaheuristic algorithms have gained the attention of researchers due to their lesser complexity and simplicity. PSO may be a promising method for FS and an interesting topic for future works in SG security. The GA emulates biological evolution and Darwinian selection [36]. The evolution mechanism of living beings is believed to follow natural selection, i.e., living species that are better suited to their environment thrive, whereas species that are at a disadvantage in their environment go extinct. Following the same principle, GA improves a given solution by incrementally choosing better possible solutions, while eliminating worse solutions. The quality of each solution is calculated using a fitness value function based on the objective function. The \(m\)-dimensional set of SE-MF vector data in \(\mathbb{R}^{n}\) is given as input to GA as follows:  
\[\left\{ \begin{array}{l}X_{1}^{(m)},\quad X_{2}^{(m)}\quad,..., \quad X_{k}^{(m)}\end{array} \right\}\] (12) _where_ \[ \begin{array}{l}X_{i}^{(m)}=\left[\begin{array}{cccc}x_{1}&x_{2}&,..., \quad x_{m-1}&x_{m}\end{array}\right],\\ \forall i\in\left\{1,2,...,k\right\}.\end{array} \]  
GA yields a set of \(n\)-dimensional vectors in subspace \(\mathbb{R}^{n}\), described as:  
\[ \begin{array}{l}\left\{\begin{array}{l}X_{1}^{(n)},\quad X_{2}^{(n)} \quad,...,\quad X_{k}^{(n)}\end{array}\right\}\\ \mbox{\emph{where}}\quad X_{i}^{(n)}=\left[\begin{array}{cccc}x_{1}&x_{2}&,..., \quad x_{n-1}&x_{n}\end{array}\right],\\ \forall i\in\left\{1,2,...,k\right\}.\end{array}  \tag{13}\]  
It is notable that the GA reduces the dimensionality of each vector in the set without affecting the cardinality of the set of vectors in Equation (14), i.e., \(n<<m\). The selected dimensions are chosen to optimize the fitness function. Hence, \(n<<m\) denotes an instance of the feature vector in the subspace that optimizes the fitness function.