Detecting anomaly in data streams by fractal model

Detecting anomaly in data streams attracts great attention in both academic and industry communities due to its wide range application in venture analysis, network monitoring, trend analysis and so on. However, existing methods on anomaly detection suffer three problems. 1) A large number of false positive results are generated. 2) Training data are needed to build the detection model, and an appropriate time window size along with corresponding threshold has to be set empirically. 3) Both time and space overhead is usually very high. To address these limitations. We propose a fractal-model-based approach to detection of anomalies that change underlying data distribution in this paper. Both a history-based algorithm and a parameter-free algorithm are introduced. We show that the later method consumes only limited memory and does not involve any training process. Theoretical analyses of the algorithm are presented. The experimental results on real life data sets indicate that, compared with existing anomaly detection methods, our algorithm can achieve higher precision with less space and time complexity.