## 2 Related Work
For high dimensional data, the type of distribution has to be determined not only for one parameter, but for several interdependent parameters, thus, methods of parametric statistical novelty detection are of little use for these datasets [44]. Some well-known examples of parametric approaches include the Gaussian Mixture Models (GMM) [45] and Hidden Markov Models (HMM) [46]. Non-parametric methods do not make assumptions about the data distribution, and instead rely on estimating a distribution based on the data itself [47; 48; 49]. Non-parametric methods tend to be very powerful for problems that require adaptability, and those where the underlying distribution is naturally unknown. One of the most well-known non-parametric probabilistic approaches is the Parzen Windows estimator [50]. This method has been used for novelty detection in applications such as network intrusion detection [51], oil flow data [52], and mammography image analysis [53]. Distance-based methods, including clustering [54; 55] or nearest-neighbour methods [56; 57], represent other types of techniques that can be used for performing a task equivalent to that of estimating the probability density function of data. These methods rely on well-defined distance metrics to compute the distance or similarity measure between two data points. There are various works dedicated to this subject, for example, in [58] the authors proposed a Distance-based Angular Clustering Algorithm (DACA) for wireless networks, in [32] a novel two-phase heuristic approach for solving the problem of transporting vehicles equipped with (CVRP) was introduced. Moreover, in some cases, distance-based methods are used to pre-process data, namely, to determine the feature vectors, which are then used for other classifiers [59], etc. Reconstruction-based approaches are frequently used in safety-critical applications for regression or classification purposes [36; 60]. These types of methods can autonomously model the underlying data, and when new instances are presented to the system, the reconstruction error, defined as the distance between these instances and the output of the system, can be related to the novelty score. Finally, deep learning for novelty and anomaly detection aims at learning feature representations or novelty/anomaly scores, respectively, via neural networks. A large number of deep learning methods have been introduced for novelty detection and they demonstrate significantly better performance than conventional approaches in addressing challenging detection problems in a variety of real-world applications [61; 62; 63; 64; 65]. Deep methods help largely improve the utilization of labelled normal data or some labelled anomaly data regardless of the data type, reducing the need for large-scale labelled data as in fully supervised settings [66]. This subsequently leads to more informed models and, thus, better recall rates. Deep methods are known for their ability to learn structures and relations from diverse types of data, such as high-dimensional tabular data, images, video, graphs, etc. However, deep learning approaches for novelty detection also have multiple disadvantages and weaknesses, which are explained in detail in the review [66]. A short summary of the various works related to the novelty and anomaly detection is presented in Table 1.  
Overall, previous research shows that most of the currently existing methods treat novelty and anomaly detection problems within the framework of one-class classification [67], in which one class (the specified normal or positive class) has to be distinguished from all other possibilities. However, there are some works that consider novelty detection as a multi-class task [68; 69; 70], but assume that more than one new class cannot appear interchangeably. In [11], a short review of works related to anomalies and novelties in the context of dynamic multi-class settings is given.