Anomaly detection

Many attempts have been made in the statistical and computer science communities to define an anomaly. The most prevalent ones include:

• An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism.[2]
• Anomalies are instances or collections of data that occur very rarely in the data set and whose features differ significantly from most of the data.
• An outlier is an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data.[3]
• An anomaly is a point or collection of points that is relatively distant from other points in multi-dimensional space of features.
• Anomalies are patterns in data that do not conform to a well defined notion of normal behaviour.[1]
• Let T be observations from a univariate Gaussian distribution and O a point from T. Then the z-score for O is greater than a pre-selected threshold if and only if O is an outlier.

Anomaly detection is applicable in a very large number and variety of domains, and is an important subarea of unsupervised machine learning. As such it has applications in cyber-security intrusion detection, fraud detection, fault detection, system health monitoring, event detection in sensor networks, detecting ecosystem disturbances, defect detection in images using machine vision, medical diagnosis and law enforcement.[4]

Anomaly detection was proposed for intrusion detection systems (IDS) by Dorothy Denning in 1986.[5] Anomaly detection for IDS is normally accomplished with thresholds and statistics, but can also be done with soft computing, and inductive learning.[6] Types of statistics proposed by 1999 included profiles of users, workstations, networks, remote hosts, groups of users, and programs based on frequencies, means, variances, covariances, and standard deviations.[7] The counterpart of anomaly detection in intrusion detection is misuse detection.

It is often used in preprocessing to remove anomalous data from the dataset. This is done for a number of reasons. Statistics of data such as the mean and standard deviation are more accurate after the removal of anomalies, and the visualisation of data can also be improved. In supervised learning, removing the anomalous data from the dataset often results in a statistically significant increase in accuracy.[8][9] Anomalies are also often the most important observations in the data to be found such as in intrusion detection or detecting abnormalities in medical images.

Many anomaly detection techniques have been proposed in literature.[1][10] Some of the popular techniques are:

• Statistical (Z-score, Tukey's range test and Grubbs's test)
• Density-based techniques (k-nearest neighbor,[11][12][13] local outlier factor,[14] isolation forests,[15][16] and many more variations of this concept[17])
• Subspace-,[18] correlation-based[19] and tensor-based [20] outlier detection for high-dimensional data[21]
• One-class support vector machines[22]
• Replicator neural networks,[23] autoencoders, variational autoencoders,[24] long short-term memory neural networks[25]
• Bayesian networks[23]
• Hidden Markov models (HMMs)[23]
• Minimum Covariance Determinant[26][27]
• Clustering: Cluster analysis-based outlier detection[28][29]
• Deviations from association rules and frequent itemsets
• Fuzzy logic-based outlier detection
• Ensemble techniques, using feature bagging,[30][31] score normalization[32][33] and different sources of diversity[34][35]

The performance of methods depends on the data set and parameters, and methods have little systematic advantages over another when compared across many data sets and parameters.[36][37]

Many of the methods discussed above only yield an anomaly score prediction, which often can be explained to users as the point being in a region of low data density (or relatively low density compared to the neighbor's densities). In explainable artificial intelligence, the users demand methods with higher explainability. Some methods allow for more detailed explanations:

• The Subspace Outlier Degree (SOD)[18] identifies attributes where a sample is normal, and attributes in which the sample deviates from the expected.
• Correlation Outlier Probabilities (COP)[19] compute an error vector how a sample point deviates from an expected location, which can be interpreted as a counterfactual explanation: the sample would be normal if it were moved to that location.

• ELKI is an open-source Java data mining toolkit that contains several anomaly detection algorithms, as well as index acceleration for them.
• PyOD is an open-source Python library developed specifically for anomaly detection.[38]
• scikit-learn is an open-source Python library that contains some algorithms for unsupervised anomaly detection.
• Wolfram Mathematica provides functionality for unsupervised anomaly detection across multiple data types [39]

• Anomaly detection benchmark data repository with carefully chosen data sets of the Ludwig-Maximilians-Universität München; Mirror Archived 2022-03-31 at the Wayback Machine at University of São Paulo.
• ODDS – ODDS: A large collection of publicly available outlier detection datasets with ground truth in different domains.
• Unsupervised Anomaly Detection Benchmark at Harvard Dataverse: Datasets for Unsupervised Anomaly Detection with ground truth.
• KMASH Data Repository at Research Data Australia having more than 12,000 anomaly detection datasets with ground truth.

• Change detection
• Statistical process control
• Novelty detection
• Hierarchical temporal memory