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

arXiv: https://arxiv.org/abs/2401.05800 · HTML: https://mlsanity.com/paper/2401.05800/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 61 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning](https://mlsanity.com/paper/2310.01061/) (2023)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlook](https://mlsanity.com/paper/2310.10196/) (2023)
- [Attend and Diagnose: Clinical Time Series Analysis using Attention Models](https://mlsanity.com/paper/1711.03905/) (2017)
- [Learning Graph Structures with Transformer for Multivariate Time Series Anomaly Detection in IoT](https://mlsanity.com/paper/2104.03466/) (2021)
- [Characterizing Concept Drift](https://mlsanity.com/paper/1511.03816/) (2015)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [An Empirical Survey on Long Document Summarization: Datasets, Models and Metrics](https://mlsanity.com/paper/2207.00939/) (2022)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [How Far are We from Robust Long Abstractive Summarization?](https://mlsanity.com/paper/2210.16732/) (2022)
- [Learning from data with structured missingness](https://mlsanity.com/paper/2304.01429/) (2023)
- [Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection](https://mlsanity.com/paper/2307.08390/) (2023)
- [Integrating Graphs with Large Language Models: Methods and Prospects](https://mlsanity.com/paper/2310.05499/) (2023)
- [Unraveling Privacy Risks of Individual Fairness in Graph Neural Networks](https://mlsanity.com/paper/2301.12951/) (2023)

## Built on by (most cited first, 10 of 10)

- [TimeOmni-1: Incentivizing Complex Reasoning with Time Series in Large Language Models](https://mlsanity.com/paper/2509.24803/) (2025)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [Hierarchical Multimodal LLMs with Semantic Space Alignment for Enhanced Time Series Classification](https://mlsanity.com/paper/2410.18686/) (2024)
- [Boundary-enhanced time series data imputation with long-term dependency diffusion models](https://mlsanity.com/paper/2501.06585/) (2025)
- [Securing Time Integrity in Energy IoT Against Clock Drift and Y2K38 Failures](https://mlsanity.com/paper/2601.23147/) (2026)
- [Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decomposition](https://mlsanity.com/paper/2510.00460/) (2025)
- [CLEANet: Robust and Efficient Anomaly Detection in Contaminated Multivariate Time Series](https://mlsanity.com/paper/2510.22619/) (2025)
- [Dynamic Reward Scaling for Multivariate Time Series Anomaly Detection: A VAE-Enhanced Reinforcement Learning Approach](https://mlsanity.com/paper/2511.12351/) (2025)
- [Unified Taxonomy for Multivariate Time Series Anomaly Detection using Deep Learning](https://mlsanity.com/paper/2603.18941/) (2026)
- [GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation](https://mlsanity.com/paper/2608.02366/) (2026)

## Abstract (arXiv)

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.