Mining Anomalies in Subspaces of High-Dimensional Time Series for Financial Transactional Data

Abstract

Anomaly detection for high-dimensional time series is always a difficult problem due to its vast search space. For general high-dimensional data, the anomalies often manifest in subspaces rather than the whole data space, and it requires an $O(2^N)$ O ( 2 N ) combinatorial search for finding the exact solution (i.e., the anomalous subspaces) where N denotes the number of dimensions. In this paper, we present a novel and practical unsupervised anomaly retrieval system to retrieve anomalies from a large volume of high dimensional transactional time series. Our system consists of two integrated modules: subspace searching module and time series discord mining module. For the subspace searching module, we propose two approximate searching methods which are capable of finding quality anomalous subspaces orders of magnitudes faster than the brute-force solution. For the discord mining module, we adopt a simple, yet effective nearest neighbor method. The proposed system is implemented and evaluated on both synthetic and real-world transactional data. The results indicate that our anomaly retrieval system can localize high quality anomaly candidates in seconds, making it practical to use in a production environment.