# Detection of Decision-Making Manipulation in the Pairwise Comparison Method
## 3 Preliminaries
### Machine Learning  
Machine learning (ML) is a field of artificial intelligence (AI) concerned with algorithms that can learn from the offered data without being explicitly programmed. The term itself was coined by [PERSON] [71]. The primary branches of ML include the following [72]:  
* _supervised learning_, where models are trained to predict the values of output variables (labels) based on the input variables (features) by presenting the model with labeled instances. The function that maps features to labels can be implemented using a broad spectrum of algorithms;
* _unsupervised learning_, where the instances are unlabeled, and the models instead try to learn patterns that can be discovered in the data;
* _reinforcement learning_, where the data are not explicitly labeled and the algorithm only receives a performance score to guide its actions. As _PC_ matrices can be treated as data instances, this paper mainly focuses on supervised learning. One of the most common challenges associated with this technique is to obtain accurate predictions (the pairwise comparison method can also be used for score prediction [73]) (label values), while maintaining the ability to generalize [74], i.e., to predict the values of labels for yet unseen instances or, in other words, to avoid overfitting to the training data. The standard approach to supervised learning involves splitting the dataset into the training set and the testing set at a particular proportion, e.g., 80:20. The algorithm is trained using the former. Then, the prediction quality is verified for the latter, which the algorithm has not yet seen. Various metrics can be used for this purpose, depending on the task (classification or regression) and the character of the data. Both the training set and the testing set should be representative of the entire dataset. Hence, it is expected that shuffling be performed before the division. However, this can still result in some bias; therefore, a common approach is to use k-fold cross validation, where the algorithm is trained and tested for different splits of the initial dataset [75]. Convolutional neural networks (CNNs) represent a foundational element in deep learning, exhibiting considerable capacity for processing and comprehending visual data. Inspired by the hierarchical organization of neurons in the human visual system, CNNs emulate this structure, enabling them to extract intricate features from images and other spatial data. Critical components of CNNs are as follows [76]:  
* _convolutional layers_ serve as the foundation of CNNs, functioning as feature extractors that capture patterns and structures from raw input data. These layers detect edges, textures, and other salient features by convolving learnable filters across the input, enabling the network to discern complex visual patterns. * _pooling layers_ play a pivotal role in spatial downsampling, reducing the computational burden while retaining essential information. These layers distill the most salient features through operations such as max pooling and average pooling, facilitating robustness and generalization. activation functions_ infuse nonlinearities into the network, empowering it to learn intricate mappings between input and output. Activation functions like Rectified Linear Unit (ReLU) enable CNNs to capture and model intricate relationships within data by introducing complexity and expressiveness. * _fully connected layers_ integrate the high-level features extracted by preceding layers, culminating in decision-making or classification. These layers, analogous to the brain's association areas, synthesize abstract representations into actionable insights, guiding the network's predictions. Training convolutional neural networks (CNNs) is an iterative parameter optimization process. During this process, the network learns to minimize the disparity between predicted outputs and ground truth labels.