Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Data

In this paper, we present XST-GCNN (eXplainable Spatio-Temporal Graph Convolutional Neural Network), an innovative architecture designed for processing heterogeneous and irregular Multivariate Time Series (MTS) data. Our processing architecture captures both temporal and feature dependencies within a unified spatio-temporal pipeline by leveraging a GCNN that uses a spatio-temporal graph and aims at optimizing predictive performance and explainability. For graph estimation, we propose several techniques, including a novel approach based on the (heterogeneous) Gower distance. Once the graphs are estimated, we propose two approaches for graph construction: one based on the Cartesian product that treats temporal instants homogeneously, and a spatio-temporal approach that considers different graphs per time step. Finally, we propose two GCNN architectures: a standard GCNN with a normalized adjacency matrix and a higher-order polynomial GCNN. In addition to predictive performance, we incorporate intrinsic explainability through architectural design choices, complemented by post hoc analysis using GNNExplainer, aimed at identifying key feature-time combinations that drive the model's predictions. We evaluate XST-GCNN using real-world Electronic Health Record data from the University Hospital of Fuenlabrada to predict Multidrug Resistance (MDR) in Intensive Care Unit patients, a critical healthcare challenge associated with high mortality and complex treatments. Our architecture outperforms traditional models, achieving a mean Receiver Operating Characteristic Area Under the Curve score of $\bf{81.03} \pm \mathbf{2.43}$ . Additionally, the explainability analysis provides actionable insights into clinical factors driving MDR predictions, enhancing model transparency and trust. This work sets a new benchmark for addressing complex inference tasks with heterogeneous and irregular MTS, offering a versatile and interpretable solution for real-world applications.