Learning interpretable dynamics: Influence-based clustering of energy consumption time series

Abstract

Energy consumption is governed by dynamic temporal patterns, context, and user behavior. Traditional clustering methods, often operating on raw data, struggle to capture evolving feature relationships and provide interpretable subgroup definitions. To overcome these limitations, we propose a novel framework, Dynamic Influence-Based Clustering, that leverages explainable machine learning (XML) to transform time-series data into an interpretable influence space. Unlike existing approaches that apply XML post-hoc or treat clustering and explanation separately, our framework is the first to jointly optimize influence representation generation and dynamic clustering within a unified mathematical framework. In this space, each data point is represented by a vector of feature contributions to an energy usage prediction, estimated using robust attribution methods such as SHAP or Integrated Gradients applied to predictive models like gradient boosting machines or neural networks. We then introduce a dynamic clustering algorithm that optimizes a composite objective balancing cluster cohesion in the influence space with novel constraints for temporal continuity and contextual alignment—capabilities entirely absent from existing clustering methods. This integrated design enables the robust detection of evolving consumer subgroups and facilitates subgroup transition analysis and anomaly detection. Extensive experiments on two real-world energy datasets demonstrate that our framework produces demonstrably more interpretable, stable, and coherent clusters compared to both standard clustering on raw features and state-of-the-art time-series clustering baselines. The proposed framework provides actionable insights into dynamic energy usage and offers a rigorous foundation for developing interpretable learning systems in time-sensitive domains.