Low-Rank Methods in Event Detection With Subsampled Point-to-Subspace Proximity Tests

Abstract

Monitoring of streamed data to detect abnormal behaviour (variously known as event detection, anomaly detection, change detection, or outlier detection) underlies many applications, especially within the Internet of Things. There, one often collects data from a variety of sources, with asynchronous sampling, and missing data. In this setting, one can detect abnormal behavior using low-rank techniques. In particular, we assume that normal observations come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise. Correspondingly, we aim to recover a representation of the subspace, and perform event detection by running point-to-subspace distance query for incoming data. We use a variant of low-rank factorisation, which considers interval uncertainty sets around “known entries”, on a suitable flattening of the input data to obtain a low-rank model. On-line, we compute the distance of incoming data to the low-rank normal subspace and update the subspace to keep it consistent with the seasonal changes present. For the distance computation, we consider subsampling. We bound the one-sided error as a function of the number of coordinates employed. In our computational experiments, we test the proposed algorithm on induction-loop data from Dublin, Ireland.

Keywords

• Multidimensional signal processing
• monitoring
• matrix completion
• point-to-subspace proximity
• probably approximately correct learning