Electrical load modeling and forecasting are critically important in the electrical network and smart grid. The sparse Bayesian Learning (SBL) algorithm can be utilized to model and forecast the electrical load behavior. The SBL algorithm can solve a sparse weight vector with respect to a kernel matrix for modeling electricity consumption. However, traditional SBL can only handle an electricity consumption record of one user at a time period. In this paper, we propose a joint SBL algorithm to model and forecast multi-users electricity consumption at multiple time periods. The spatial and historical similarity in multi-users electricity consumption records are exploited and integrated in the joint SBL algorithm for accurate prediction and good modeling. Experimental results based on real data show that the proposed joint SBL algorithm can produce much better prediction accuracy than the traditional SBL algorithm.
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