  This paper addresses the challenge of online multi-source domain adaptation
(MSDA) in transfer learning, a scenario where one needs to adapt multiple,
heterogeneous source domains towards a target domain that comes in a stream. We
introduce a novel approach for the online fit of a Gaussian Mixture Model
(GMM), based on the Wasserstein geometry of Gaussian measures. We build upon
this method and recent developments in dataset dictionary learning for
proposing a novel strategy in online MSDA. Experiments on the challenging
Tennessee Eastman Process benchmark demonstrate that our approach is able to
adapt \emph{on the fly} to the stream of target domain data. Furthermore, our
online GMM serves as a memory, representing the whole stream of data.
