Aggregation procedure of Gaussian Mixture Models for additive features

In this work we provide details on a new and effective approach able to generate Gaussian Mixture Models (GMMs) for the classification of aggregated time series. More specifically, our procedure can be applied to time series that are aggregated together by adding their features. The procedure takes advantage of the additive property of the Gaussians that complies with the additive property of the features. Our goal is to classify aggregated time series, i.e. we aim to identify the classes of the single time series contributing to the total. The standard approach consists in training the models using the combination of several time series coming from different classes. However, this has the drawback of being a very slow operation given the amount of data. The proposed approach, called GMMs aggregation procedure, addresses this problem. It consists of three steps: (i) modeling the independent classes, (ii) generation of the models for the class combinations and (iii) simplification of the generated models. We show the effectiveness of our approach by using time series in the context of electrical appliance consumption, where the time series are aggregated by adding the active and reactive power. Finally, we compare the proposed approach with the standard procedure.