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

TL;DR

XST-GCNN (eXplainable Spatio-Temporal Graph Convolutional Neural Network), an innovative architecture designed for processing heterogeneous and irregular Multivariate Time Series data, is presented, setting a new benchmark for addressing complex inference tasks with heterogeneous and irregular MTS.

Abstract

In this paper, we present XST-GCNN (eXplainable Spatio-Temporal Graph Convolutional Neural Network), a novel architecture for processing heterogeneous and irregular Multivariate Time Series (MTS) data. Our approach captures temporal and feature dependencies within a unified spatio-temporal pipeline by leveraging a GCNN that uses a spatio-temporal graph aimed at optimizing predictive accuracy and interoperability. For graph estimation, we introduce techniques, including one based on the (heterogeneous) Gower distance. Once estimated, we propose two methods for graph construction: one based on the Cartesian product, treating temporal instants homogeneously, and another spatio-temporal approach with distinct graphs per time step. We also propose two GCNN architectures: a standard GCNN with a normalized adjacency matrix and a higher-order polynomial GCNN. In addition to accuracy, we emphasize explainability by designing an inherently interpretable model and performing a thorough interpretability analysis, identifying key feature-time combinations that drive predictions. We evaluate XST-GCNN using real-world Electronic Health Record data from University Hospital of Fuenlabrada to predict Multidrug Resistance (MDR) in ICU patients, a critical healthcare challenge linked to high mortality and complex treatments. Our architecture outperforms traditional models, achieving a mean ROC-AUC score of 81.03 +- 2.43. Furthermore, the interpretability analysis provides actionable insights into clinical factors driving MDR predictions, enhancing model transparency. This work sets a benchmark for tackling complex inference tasks with heterogeneous MTS, offering a versatile, interpretable solution for real-world applications.

Figures (5)

• Figure 1: Proposed XST-GCNN architecture for inference tasks using irregular MTS and heterogeneous features. The architecture employs relatively advanced SP techniques, including graph estimation based on correlations, smoothness constraints, and distance measures such as HGD and DTW. The graph representation is modeled as an STG or CPG, capturing both temporal and spatial dependencies. Two definitions for the GCNN layer are proposed: Standard GCNNs with Normalized Adjacency and Higher-Order Polynomial GCNNs. These layers are followed by LeakyReLU activation and dropout layers before passing through Fully Connected (FC) layers and a sigmoid activation for the final inference task. The architecture also emphasizes explainability, incorporating both pre-hoc and intrinsic methods. Pre-hoc explainability is achieved through node importance analysis during the graph representation and estimation phases. Intrinsic explainability is provided through analysis on both real and synthetic data during and after the architecture training. This includes the consideration of synthetic Kronecker delta signals to assess the sensitivity of the architecture with respect to each of the inputs. The combined approach put forth contributes to improved decision-making and a deeper understanding of the model's behavior.
• Figure 2: Bar graph depicts the frequency distribution of variables associated with MDR (green) and non-MDR (blue) cases across a range of clinical features. The x-axis represents different clinical variables, while the y-axis indicates the frequency of occurrence for each variable. This visual comparison highlights the prevalence and variation of specific clinical features between MDR and non-MDR groups, providing insights into potential risk factors and patterns associated with MDR.
• Figure 3: Adjacency matrices representing the estimated graphs for the CPG using three different methods: correlation, smoothness, and DTW-HGW (from left to right in each row). The rows correspond to different threshold levels, ranging from 0.6 to 0.975 in increments of 0.125, from top to bottom.
• Figure 4: Overview of the variables utilized in this study for the real-world application case. The dataset comprises heterogeneous variables, categorized into binary variables (highlighted in blue) and continuous variables (highlighted in green). Each variable is annotated with its respective identifier for precise reference.
• Figure 5: Temporal evolution of estimated graphs using the HGD method. Each row represents a graph at a specific time step, illustrating the changing connectivity patterns between variables over time. Nodes correspond to distinct clinical variables, with edges indicating the relationships and dependencies captured at each graph temporally. This visualization enables analysis of the dynamics in variable importance and interaction, providing valuable insights for MDR prediction.