Anomaly detection in scientific data using joint statistical moments

TL;DR

This paper introduces a novel anomaly detection method for multivariate scientific data using high-order joint moments, specifically kurtosis, to identify outliers and anomalous events in spatial and temporal domains.

Contribution

The paper proposes a new approach leveraging principal kurtosis vectors derived from joint cumulant tensors for efficient anomaly detection in scientific data.

Findings

Effective detection of auto-ignition events in combustion data

Principal kurtosis vectors reveal key directions of outliers

Algorithm accurately identifies spatial and temporal anomalies

Abstract

We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. The algorithm decomposes the data into several spatial sub-domains and time steps to identify regions with such events. Feature moment metrics, based on the alignments of the principal kurtosis vectors, are computed at each sub-domain and time step for all features to quantify their relative importance towards the overall kurtosis in the data. Accordingly, spatial and temporal anomaly metrics for each sub-domain are proposed using the Hellinger distance of the feature moment metric distribution from a suitable nominal distribution. We apply the algorithm to a one-dimensional turbulent auto-ignition combustion case and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps.