New Anomaly Detection Method based on the Multivariate Generalized Pareto Distributions

Abstract

The extreme events of floods, rainfalls, waves, and wind often cause serious damage. The observed data can be used to detect the sign of abnormal phenomena and can prevent the crucial damage. Anomaly detection techniques, the techniques of distinguishing between normal and abnormal cases from the data, have been one of the most used methods for detecting suspicious events from the collected data. Although many methods of the anomaly detection have appeared in the literature, almost all of them are based on multivariate statistical process control techniques and machine learning techniques. Recently, under the idea that information for suspicious and critical events is more likely to be involved in the largest or smallest values than values around the mean or median, the anomaly detection methods are based on the “Extreme Value Theory” (EVT), which is the statistical theory dealing with the largest or smallest data, attract the variety of areas. However, they can be applied to only univariate data since they have been based on the EVT for univariate data, and hence there has been little work for the multivariate anomaly detection based on the EVT. The multivariate anomaly detection method is important in applications because almost all data for anomaly detection are multivariate and can be misleading by applying univariate methods to multivariate data independently. In this paper, we propose the new anomaly detection method based on the multivariate EVT. The performance of the proposed methods is evaluated by the Monte Carlo simulation. To illustrate all the proposed methods of anomaly detection for multivariate data, we apply them to analyze the new real data of precipitation events in 2021. The numerical results show that the proposed method outperforms the existing methods.