![]() Bernoulli seems to be the first to address the issue in 1777, with subsequent theory building throughout the 1800s, 1900s and beyond. Outlier research has a long history and traditionally focused on techniques for rejecting or accommodating the extreme cases that hamper statistical inference. Anomaly detection (AD) is the process of analyzing the data to identify these unusual occurrences. Identifying them can be a difficult task due to the many shapes and sizes they come in, as illustrated in Fig. Although anomalies can form a noise factor hindering the data analysis, they may also constitute the actual signals that one is looking for. Anomalies are assumed to be both rare and different, and pertain to a wide variety of phenomena, which include static entities and time-related events, single (atomic) cases and grouped (aggregated) cases, as well as desired and undesired observations. Such occurrences are often also referred to as outliers, novelties, deviants or discords. The term anomalies in this context refers to cases, or groups of cases, that are in some way unusual and deviate from some notion of normality. ![]() These large collections of data are mined in both academia and practice, with the aim of identifying patterns as well as peculiarities. Owing to the massive data collection taking place in the current era and the imperfect measurement systems used for this, anomalous observations can thus be expected to be amply present in our datasets. Although rare by definition, such strange and unusual occurrences can actually also said to be relatively abundant due to the huge amount of objects and interactions in the world. The physical and social world is known to bring about abnormal and bizarre phenomena that are seemingly hard to explain. The typology facilitates the evaluation of the functional capabilities of anomaly detection algorithms, contributes to explainable data science, and provides insights into relevant topics such as local versus global anomalies. These fundamental and data-centric dimensions naturally yield 3 broad groups, 9 basic types, and 63 subtypes of anomalies. To concretely define the concept of the anomaly and its different manifestations, the typology employs five dimensions: data type, cardinality of relationship, anomaly level, data structure, and data distribution. By means of an extensive literature review this study therefore offers the first theoretically principled and domain-independent typology of data anomalies and presents a full overview of anomaly types and subtypes. Moreover, despite some 250 years of publications on the topic, no comprehensive and concrete overviews of the different types of anomalies have hitherto been published. The concept of the anomaly is typically ill defined and perceived as vague and domain-dependent. ![]() Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns.
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