On the Nature and Types of Anomalies: A Review

Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. The concept of the anomaly is generally ill-defined and perceived as vague and domain-dependent. 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. 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. 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. These fundamental and data-centric dimensions naturally yield 3 broad groups, 9 basic types and 61 subtypes of anomalies. 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.Comment: 38 pages (30 pages content), 10 figures, 3 tables. Preprint; review comments will be appreciated. Improvements in version 2: Explicit mention of fifth anomaly dimension; Added section on explainable anomaly detection; Added section on variations on the anomaly concept; Various minor additions and improvement

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201