## 4 Materials and Methods
### Anomaly Detection AI Algorithms  
The domain of AI extends to the field of Anomaly Detection (AD), encompassing a variety of approaches. Specifically, it ranges from unsupervised to supervised learning and even includes DL algorithms. In this subsection, we provide a brief review of the most common approaches. As mentioned in the previous section, this work focuses on the case study of fraud detection, which is a category within AD. The choice of this domain is driven by two specific reasons:  
1. Environmental impact: While there are AI sectors with more significant emissions, it is important to also pay attention to other sectors, such as AD, which will be demonstrated to have a non-negligible environmental impact. 2. Data accessibility: This study uses a dataset provided by an Italian bank containing both fraudulent and non-fraudulent banking transactions. Access to a real dataset, rather than a synthetic one, allows for more realistic evaluations and assessments. As mentioned earlier, this case study employs supervised learning algorithms. In supervised learning, labelled datasets are used, where each record is labelled as either a fraudulent or non-fraudulent transaction. In contrast, unsupervised learning uses unlabelled records and allows them to form clusters autonomously. * Isolation Forest (IF) [33]. This algorithm is used in AD to identify anomalies within a dataset. It is based on an unsupervised learning approach and operates on the principle that anomalies are rarer and therefore more \"isolated\" than normal instances. The algorithm works by creating a set of random decision trees, known as isolation trees. Each tree is constructed by randomly selecting a subset of the data and recursively partitioning it based on random attribute values. The splitting process continues until each data instance is isolated in a single terminal node of the tree. To identify anomalies, the algorithm evaluates the separation path within the trees. Instances that require fewer splits to be isolated are considered more anomalous. Therefore, anomalies will have a shorter average path length compared with normal instances. The Isolation Forest has several advantageous features, including its ability to handle large-scale datasets efficiently, robustness to variations in data dimensionality, and capability to detect different types of anomalies, such as point anomalies and collective anomalies. However, it is important to note that the Isolation Forest may not be effective in detecting certain complex or subtle anomalies that require more contextual analysis. Thus, it is often used in combination with other AD algorithms to improve overall system performance. Support Vector Machine (SVM) [34]. This is a ML algorithm used for classification and regression problems. It is a supervised learning model that can separate data examples into different classes. The basic idea of an SVM is to find the optimal hyperplane that divides the feature space to maximise the separation between different data classes. The hyperplane is selected to be the maximum distance from a set of training examples of one class (called support vectors) while maximising the distance from the support vectors of the other classes. In practice, an SVM uses a set of labelled training examples to train a model that can subsequently classify new unlabelled examples. During the training phase, the SVM algorithm optimises an objective function that balances the maximum separation between classes with the reduction of classification error. The use of kernel functions is an important aspect of SVMs. A kernel allows data to be mapped into a high-dimensional feature space, where it is easier to find a linearly separating hyperplane. This enables SVMs to address nonlinear classification problems. SVMs have proven effective in a variety of applications, including image recognition, text analysis, bioinformatics, and more. They are known for their ability to handle large datasets and generalise well even on unseen data during training. * HF-SCA [35].