Combinatorial commutative algebra and its application on appliance identification

Non-Intrusive Load Monitoring (NILM) involves identifying and analyzing electrical loads through monitoring fluctuations in physical parameters like voltage and current. The escalating diversity and quantity of modern electrical devices have underscored the critical need for effective feature extraction and robust classification modeling in NILM. While deep learning has advanced feature extraction, these methods often produce features with ambiguous mathematical meanings and high computational costs. This study introduces h-vectors from combinatorial commutative algebra as a novel feature extraction tool for NILM. By leveraging mathematical principles, this approach rapidly extracts nonlinear, shape-based features from active power signals, offering clear interpretability. Experimental validation on the PLAID public dataset reveals that our method achieves faster load identification while significantly improving accuracy for complex appliances compared to state-of-the-art techniques. Thus, the proposed framework represents a balanced NILM solution, harmonizing computational efficiency, accuracy, and interpretability—a key advancement for practical deployment.