Missing data imputation using mixture factor analysis for building electric load data

We propose a mixture factor analysis (MFA) method for estimating missing values in building electric load data. Buildings consume a tremendous amount of energy. Thanks to the recent advances in data technologies such as machine learning and applied statistics, data-driven approaches to making buildings more energy-efficient become a major research area. However, building electric load data suffer from quality issues due to data missing originated from malfunctioning sensors, network stability, and other environmental causes. We note that data missing can occur even under advanced Internet Technology (IT) systems such as energy information systems (EIS) and energy management systems (EMS) due to signal stability and low-speed computers. The existence of missing data may significantly affect building operations, causing inaccuracy in evaluating building status and forecasting future electric demands. In this respect, dealing with missing data problems should be as important as developing highly accurate forecasting algorithms. While investigating load data, we find that building electric loads exhibit distinct patterns with cyclic rotations that we can take advantage of in both model design and selection stages. Motivated by the finding, unlike the previous studies designed for general time-series data, we propose a novel data imputation model to represent patterns and their cyclic rotations in electric load data. Simulation studies reveal that the proposed model works well when the time window size is a divisor of the cycle length, which significantly reduces model selection efforts. Numerical results with two real data sets justify our findings and the performance of the proposed approach against benchmark methods.