Detection of energy waste in French households thanks to a co-clustering model for multivariate functional data

The exponential growth of smart devices in all aspects of everyday life leads to make common the collection of high frequency data. Those data can be seen as multivariate functional data: quantitative entities evolving along time, for which there is a growing needs of methods to summarize and understand them. The database that have motivated our project is supplied by the historical French electricity provider whose aim is to detect poorly insulated buildings, anomalies or long periods of absence. Their motivation is to answer COP24 requirements to reduce energy waste and to adapt electric load. To this end, a novel co-clustering model for multivariate functional data is defined. The model is based on a functional latent block model which assumes for each block a probabilistic distribution for multivariate functional principal component scores. A Stochastic EM algorithm, embedding a Gibbs sampler is proposed for model inference, as well as model selection criteria for choosing the number of co-clusters.