An explainable deep learning method based on spectral co-clustering for ozone time series forecasting

Abstract Tropospheric ozone forecasting is critical for public health, yet the deep learning models that achieve high accuracy often function as black boxes. This lack of transparency, along with the inability of popular explainability techniques like SHapley Additive exPlanations (SHAP) to capture essential temporal dependencies, limits their practical utility and trustworthiness in environmental management. To address this, we propose a novel framework, eXplainable Deep Learning with Spectral Co-clustering for Time Series, that integrates spectral co-clustering to enhance forecasting performance and provide post-hoc structured interpretability for air-quality time series. The methodology comprises data preprocessing, feature engineering (including lagging, rolling statistics, and time-based features), and deep learning architectures (Multilayer Perceptron, Gated Recurrent Unit, and hybrid models). Bayesian optimization is used to fine-tune hyperparameters. The core contribution is a spectral co-clustering technique that simultaneously partitions features and time instances into co-clusters, revealing critical inter-feature relationships and temporal patterns that drive predictions. The framework was rigorously validated through extensive experiments on data from five air quality monitoring stations. The proposed approach achieved RMSE values ranging from 0.73 to 6.08, significantly outperforming existing methods, including a temporal LSTM baseline, with performance improvements of approximately 59.19% to 95.65%. Results demonstrate that the proposed approach not only achieves high forecasting accuracy but also, through post-hoc heatmap visualizations of the objectively selected best-performing co-cluster, identifies the key features and time periods governing model predictions, thereby offering an interpretable understanding of the temporal and feature-level drivers associated with ozone variability. Thus, a transparent and effective solution for ozone forecasting is proposed, with a modular design generalizable to other environmental time series prediction tasks.