Anomaly detection using piecewise aggregate approximation in the amplitude domain

Anomaly detection has received much attention due to its various applications. Generally, the first step to discover anomalies is a data representation method which reduces dimensionality as well as preserves key information. Anomaly detection based on real-value representation methods is meaningful for its convenience in numeric operation. A typical real-value representation method is the Piecewise Aggregate Approximation (PAA) that is simple and intuitive by capturing mean values of segments in a sequence. However, if segments are same or similar in their average values but different in their oscillation amplitudes, the PAA method is ineffective to describe a sequence composed of such segments. To address this issue, we propose a representation method called the Piecewise Aggregate Approximation in the Amplitude Domain (AD-PAA). For discovering anomalies, a sequence is partitioned into subsequences by a sliding window firstly. Then in the AD-PAA method, a subsequence is divided into equal size subsections according to the amplitude domain. With mean values of subsections computed, the amplitude oscillation of a subsequence is embodied effectively. When the AD-PAA method is applied to approximate subsequences, the AD-PAA representation of a sequence is constructed. Anomalies are determined by anomaly scores that are based on similarities among representation results. Experimental results on various data confirm that the proposed method is more accurate than the PAA based method and other comparison methods. The ability to differentiate anomalies of the proposed algorithm is also superior.