Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values

TL;DR

GST-Pro addresses anomaly detection in irregular multivariate time series with missing values by combining a Dynamic Graph Neural Controlled Differential Equation (DG-NCDE) forecaster with a distribution-based anomaly scorer. The DG-NCDE jointly models spatial and temporal dependencies through a spatial NCDE and a temporal NCDE, working on continuously interpolated paths to handle missing data. The anomaly scorer relies on forecast statistics, is parameter-free, and operates online without access to current ground-truth observations. Empirical results on SWaT and WADI show state-of-the-art performance under both irregular and regular sampling, with strong robustness to high missing rates, demonstrating practical applicability to real-world systems.

Abstract

The detection of anomalies in multivariate time series data is crucial for various practical applications, including smart power grids, traffic flow forecasting, and industrial process control. However, real-world time series data is usually not well-structured, posting significant challenges to existing approaches: (1) The existence of missing values in multivariate time series data along variable and time dimensions hinders the effective modeling of interwoven spatial and temporal dependencies, resulting in important patterns being overlooked during model training; (2) Anomaly scoring with irregularly-sampled observations is less explored, making it difficult to use existing detectors for multivariate series without fully-observed values. In this work, we introduce a novel framework called GST-Pro, which utilizes a graph spatiotemporal process and anomaly scorer to tackle the aforementioned challenges in detecting anomalies on irregularly-sampled multivariate time series. Our approach comprises two main components. First, we propose a graph spatiotemporal process based on neural controlled differential equations. This process enables effective modeling of multivariate time series from both spatial and temporal perspectives, even when the data contains missing values. Second, we present a novel distribution-based anomaly scoring mechanism that alleviates the reliance on complete uniform observations. By analyzing the predictions of the graph spatiotemporal process, our approach allows anomalies to be easily detected. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods, regardless of whether there are missing values present in the data. Our code is available: https://github.com/huankoh/GST-Pro.

Figures (4)

• Figure 1: A simplified comparison of multivariate time series data with complete values (left) and missing values (right). First 6 observations are the normal data used for unsupervised training and the last 6 are to test a model in detecting anomaly events. Red circles indicate that it is an anomalous observation as manifested by four middle observations in the complete test data.
• Figure 2: Overall Framework of GST-Pro. (a): Imputing discrete observations with missing values to generate continuous paths. (b): Utilizing two neural controlled differential equations to process input signals from both spatial and temporal perspectives. (c): Conducting real-time anomaly detection on arbitrary multivariate time series using a distribution-based scorer that assesses anomalies based on forecast outputs, without ground-truth observations. Anomaly scores are calculated by evaluating the likelihood of deviations in current forecasts from historical forecasts using a multivariate normal distribution.
• Figure 3: ROC-AUC performances on SWaT and WADI. TPR and FPR represents True and False Positive Rate. GST-Pro achieves state-of-the-art results with ROC-AUC 0.854 and 0.733 on SWaT and WADI.
• Figure 4: ROC-AUC and PRC-AUC performances on SWaT and WADI from 10% to 90% missing rate. GST-Pro still achieves state-of-the-art ROC-AUC results at 70% missing rate on SWaT (0.856) and 90% on WADI (0.629), as compared to the best competing baseline on regular MTS Anomaly Detection setting in Figure \ref{['fig. roc_auc']}.