Cross-environment activity recognition in smart homes is a very challenging problem, specially for data-driven approaches. Currently, systems developed to work for a certain environment degrade substantially when applied to a new environment, where not only sensors, but also the monitored activities may be different. Some systems require manual labeling and mapping of the new sensor names and activities using an ontology. Ideally, given a new smart home, we would like to be able to deploy the system, which has been trained on other sources, with minimal manual effort and with acceptable performance. In this paper, we propose the use of neural word embeddings to represent sensor activations and activities, which comes with several advantages: (i) the representation of the semantic information of sensor and activity names, and (ii) automatically mapping sensors and activities of different environments into the same semantic space. Based on this novel representation approach, we propose two data-driven activity recognition systems: the first one is a completely unsupervised system based on embedding similarities, while the second one adds a supervised learning regressor on top of them. We compare our approaches with some baselines using four public datasets, showing that data-driven cross-environment activity recognition obtains good results even when sensors and activity labels significantly differ. Our results show promise for reducing manual effort, and are complementary to other efforts using ontologies. (C) 2020 Elsevier B.V. All rights reserved.