This post is summary of the “Anomaly Detection : A Survey”. Anomaly detection refers to the problem of finding patterns in data that do not conform to expected behavior. These non-conforming patterns are often referred to as anomalies, outliers, discordant observations, exceptions, aberrations, surprises, peculiarities or contaminants in different application domains.

Anomalies are patterns in data that do not conform to a well defined notion of normal behavior.

• Interesting to analyze
• Unwanted noise in the data also can be found in there.
• Novelty detection which aims at detecting previously unobserved (emergent, novel) patterns in the data

Challenges for Anomaly Detection

• Drawing the boundary between normal and anomalous behavior
• Availability of labeled data
• Noisy data

Type of Anomaly
Anomalies can be classified into following three categories

1. Point Anomalies - An individual data instance can be considered as anomalous with respect to the rest of data
2. Contextual Anomalies - A data instance is anomalous in a specific context (but not otherwise), then it is termed as a contextual anomaly (also referred as conditional anomaly). Each data instance is defined using following two sets of attributes
• Contextual attributes. The contextual attributes are used to determine the context (or neighborhood) for that instance
  eg:
  In time- series data, time is a contextual attribute which determines the position of an instance on the entire sequence
• Behavioral attributes. The behavioral attributes define the non-contextual characteristics of an instance
  eg:
  In a spatial data set describing the average rainfall of the entire world, the amount of rainfall at any location is a behavioral attribute
• To explain this we will look into "Exchange Rate History For Converting United States Dollar (USD) to Sri Lankan Rupee (LKR)"[1]

Contextual anomaly t2 in a exchange rate time series. Note that the exchange rate at time t1 is same as that at time t2 but occurs in a different context and hence is not considered as an anomaly
     3.    Collective Anomalies - A collection of related data instances is anomalous with respect to the entire data set

Data Labels
The labels associated with a data instance denote if that instance is normal or anomalous. Depending labels availability, anomaly detection techniques can be operated in one of the following three modes

1. Supervised anomaly detection - Techniques trained in supervised mode assume the availability of a training data set which has labeled instances for normal as well as anomaly class
2. Semi-Supervised anomaly detection - Techniques that operate in a semi-supervised mode, assume that the training data has labeled instances for only the normal class. Since they do not require labels for the anomaly class
3. Unsupervised anomaly detection - Techniques that operate in unsupervised mode do not require training data, and thus are most widely applicable. The techniques  implicit assume that normal instances are far more frequent than anomalies in the test data. If this assumption is not true then such techniques suffer from high false alarm rate

Output of Anomaly Detection
Anomaly detection have two types of output techniques

1. Scores. Scoring techniques assign an anomaly score to each instance in the test data depending on the degree to which that instance is considered an anomaly
2. Labels. Techniques in this category assign a label (normal or anomalous) to each test instance

Applications of Anomaly Detection
Intrusion detection
Intrusion detection refers to detection of malicious activity. The key challenge for anomaly detection in this domain is the huge volume of data. Thus, semi-supervised and unsupervised anomaly detection techniques are preferred in this domain.Denning[3] classifies intrusion detection systems into host based and net-
work based intrusion detection systems.

• Host Based Intrusion Detection Systems  - This deals with operating system call traces
• Network Intrusion Detection Systems - These systems deal with detecting intrusions in network data. The intrusions typically occur as anomalous patterns (point anomalies) though certain techniques model[4] the data in a sequential fashion and detect anomalous subsequences (collective anomalies). A challenge faced by anomaly detection techniques in this domain is that the nature of anomalies keeps changing over time as the intruders adapt their network attacks to evade the existing intrusion detection solutions.

Fraud Detection

Fraud detection refers to detection of criminal activities occurring in commercial organizations such as banks, credit card companies, insurance agencies, cell phone companies, stock market, etc. The organizations are interested in immediate detection of such frauds to prevent economic losses.  Detection techniques used for credit card fraud and network intrusion detection as below.

• Statistical Profiling using Histograms
• Parametric Statistical Modeling
• Non-parametric Statistical Modeling Bayesian Networks
• Neural Networks
• Support Vector Machines
• Rule-based
• Clustering Based
• Nearest Neighbor based
• Spectral
• Information Theoretic

Here are some domain in fraud detections

• Credit Card Fraud Detection
• Mobile Phone Fraud Detection
• Insurance Claim Fraud Detection
• Insider Trading Detection

Medical and Public Health Anomaly Detection
Anomaly detection in the medical and public health domains typically work with pa- tient records. The data can have anomalies due to several reasons such as abnormal patient condition or instrumentation errors or recording errors. Thus the anomaly detection is a very critical problem in this domain and requires high degree of accuracy.
Industrial Damage Detection
Such damages need to be detected early to prevent further escalation and losses.
Fault Detection in Mechanical Units
Structural Defect Detection
Image Processing
Anomaly detection techniques dealing with images are either interested in any changes in an image over time (motion detection) or in regions which appear ab- normal on the static image. This domain includes satellite imagery.
Anomaly Detection in Text Data
Anomaly detection techniques in this domain primarily detect novel topics or events or news stories in a collection of documents or news articles. The anomalies are caused due to a new interesting event or an anomalous topic.
Sensor Networks
Since the sensor data collected from various wireless sensors has several unique characteristics.

References
[1] http://themoneyconverter.com/USD/LKR.aspx
[2] Varun Chandola, Arindam Banerjee, and Vipin Kumar. 2009. Anomaly detection: A survey. ACM Comput. Surv. 41, 3, Article 15 (July 2009), 58 pages. DOI=10.1145/1541880.1541882 http://doi.acm.org/10.1145/1541880.1541882
[3] Denning, D. E. 1987. An intrusion detection model. IEEE Transactions of Software Engineer-ing 13, 2, 222–232.
[4]Gwadera, R., Atallah, M. J., and Szpankowski, W. 2004. Detection of significant sets of episodes in event sequences. In Proceedings of the Fourth IEEE International Conference on Data Mining. IEEE Computer Society, Washington, DC, USA, 3–10.