By Charu C. Aggarwal

- Basic algorithms: Chapters 1 via 7 talk about the basic algorithms for outlier research, together with probabilistic and statistical tools, linear equipment, proximity-based tools, high-dimensional (subspace) tools, ensemble tools, and supervised methods.
- Domain-specific tools: Chapters eight via 12 speak about outlier detection algorithms for varied domain names of information, corresponding to textual content, specific facts, time-series info, discrete series facts, spatial info, and community data.
- Applications: bankruptcy thirteen is dedicated to varied purposes of outlier research. a few information is usually supplied for the practitioner.

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As in the case of autoregressive models of continuous data, it is possible to use (typically Markovian) prediction-based techniques to forecast the value of a single position in the sequence. Deviations from forecasted values are identiﬁed as contextual outliers. It is often desirable to perform the prediction in real time in these settings. In other cases, anomalous events can be identiﬁed only by variations from the normal patterns exhibited by the subsequences over multiple time stamps. This is analogous to the problem of unusual shape detection in time-series data, and it represents a set of collective outliers.

This is referred to as the Positive-Unlabeled Classiﬁcation (PUC) problem in machine learning. This variation is still quite similar to the fully supervised rare-class scenario, except that the classiﬁcation model needs to be more cognizant of the contaminants in the negative (unlabeled) class. • Only instances of a subset of the normal and anomalous classes may be available, but some of the anomalous classes may be missing from the training data [388, 389, 538]. Such situations are quite common in scenarios such as intrusion detection in which some intrusions may be known, but other new types of intrusions are continually discovered over time.

For example, network intrusion events may cause aggregate change points in a network stream. On the other hand, individual point novelties may or may not correspond to aggregate change points. The latter case is similar to multidimensional anomaly detection with an eﬃciency constraint for the streaming scenario. Methods for anomaly detection in time-series data and multidimensional data streams are discussed in Chapter 9. 2 CHAPTER 1. AN INTRODUCTION TO OUTLIER ANALYSIS Discrete Sequences Many discrete sequence-based applications such as intrusion-detection and fraud-detection are clearly temporal in nature.