Independent-Variation Matrix Factorization with Application to Energy Disaggregation

Matrix factorization techniques have proven to be useful in many unsupervised learning applications. Such techniques have been recently applied to Non Intrusive Load Monitoring (NILM), the process of breaking down the total electric consumption of a building into consumptions of individual appliances. While several studies addressed the NILM problem for small-scale buildings, only few studies considered the problem for large buildings, where the signals exhibit significantly different behavior. To overcome the unaddressed difficulties of processing high frequency current signals that are measured in large buildings, we propose a novel technique called Independent-Variation Matrix Factorization (IVMF), which expresses an observation matrix as the product of two matrices: the signature and the activation. Motivated by the nature of the current signals, it uses a regularization term on the temporal variations of the activation matrix and a positivity constraint, and the columns of the signature matrix are constrained to lie in a specific set. To solve the resulting optimization problem, we rely on an alternating minimization strategy involving dual optimization and quasi-Newton algorithms. The algorithm is tested against Independent Component Analysis (ICA) and Semi Nonnegative Matrix Factorization (SNMF) on a synthetic source separation problem and on a realistic NILM application for large commercial buildings. We show that IVMF outperforms competing methods and is particularly appropriate to recover positive sources that have a strong temporal dependency and sources whose variations are independent from each other.