Learning and Adaptation to Detect Changes and Anomalies in High-Dimensional Data

Abstract

The problem of monitoring a datastream and detecting whether the data generating process changes from normal to novel and possibly anomalous conditions has relevant applications in many real scenarios, such as health monitoring and quality inspection of industrial processes. A general approach often adopted in the literature is to learn a model to describe normal data and detect as anomalous those data that do not conform to the learned model. However, several challenges have to be addressed to make this approach effective in real world scenarios, where acquired data are often characterized by high dimension and feature complex structures (such as signals and images). We address this problem from two perspectives corresponding to different modeling assumptions on the data-generating process. At first, we model data as realization of random vectors, as it is customary in the statistical literature. In this settings we focus on the change detection problem, where the goal is to detect whether the datastream permanently departs from normal conditions. We theoretically prove the intrinsic difficulty of this problem when the data dimension increases and propose a novel non-parametric and multivariate change-detection algorithm. In the second part, we focus on data having complex structure and we adopt dictionaries yielding sparse representations to model normal data. We propose novel algorithms to detect anomalies in such datastreams and to adapt the learned model when the process generating normal data changes.