Exploring energy consumption patterns in Colombian companies: a functional data clustering approach

Clustering is a form of unsupervised learning designed to group data based on its inherent structural patterns and characteristics, identified through data exploration rather than assumptions that may introduce bias.In this work, we focus on the application of a novel data-driven clustering methodology to energy consumption data, treated as an aggregated signal.By disaggregating this signal, we aim to identify relevant consumption profiles or device-level behaviors-an approach rarely applied in energy analysis.From a methodological perspective, we propose to combine both distance-based (k-means, PAM) and density-based (HDBSCAN) clustering methods, extending them from multivariate to functional data.This dual exploration offers a broader search spectrum in contrast to each individual framework or paradigm.From an algorithmic perspective, we enhance the initialization of PAM with the randomized seeding technique of k-means++ for improved performance and optimize HDBSCAN's minpts hyperparameter based on internal validation metrics (Stability Score, GLOSH Score, and Membership Probability Score) for improved robustness rather than relying on traditional empirical methods.We demonstrate the effectiveness of our methodology by applying it to both synthetic and real-world energy consumption data.Results show that while both density-based and distance-based methods could individually identify clusters under specific conditions, only the dual methodology successfully identified clusters across all synthetic settings.In the real data application, we confidently identified three distinct clusters that represent energy consumption patterns: constant, day, and night.These results highlight the potential of the methodology for clustering functional data in an arbitrary context and provide valuable insights into energy analysis.