The previous chapter discusses anomaly detection from the perspective of continuous time series. A related setting is one in which the individual elements at each time stamp are discrete-valued (i.e., categorical). Such discrete time-series are also referred to as sequences. Discrete-valued temporal scenarios arise in numerous systems diagnosis, intrusion detection, and biological applications. In some domains such as intrusion detection and systems diagnosis, the discrete sequences are caused by temporal ordering, whereas in other domains such as biological data, the discrete sequences are caused by physical ordering. Nevertheless, at a logical level, the differences in the problem definitions for the two cases are relatively minor. The primary difference is that temporal data often has a specific direction to the analysis in real scenarios (i.e., forward in time), whereas this may not be the case for data based on placement relationships. At the analytical level, the models for the two cases are different in minimal ways and typically have cross-applicability.
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