Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the di®erent directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.

This thesis deals with the problem of anomaly detection for sequence data. Anomaly detection has been a widely researched problem in several application domains such as system health management, intrusion detection, healthcare, bioinformatics, fraud detection, and mechanical fault detection. Traditional anomaly detection techniques analyze each data instance (as a univariate or multivariate record) independently, and ignore the sequential aspect of the data. Often, anomalies in sequences can be detected only by analyzing data instances together as a sequence, and hence cannot detected by traditional anomaly detection techniques. The problem of anomaly detection for sequence data is a rich area of research because of two main reasons. First, sequences can be of different types, e.g., symbolic sequences, time series data, etc., and each type of sequence poses unique set of problems. Second, anomalies in sequences can be defined in multiple ways and hence there are different problem formulations. In this thesis we focus on solving one particular problem formulation called semi-supervised anomaly detection. We study the problem