In this paper, a classifier based early warning system is designed, trained and tested based on time-series of Phasor Measurement Unit (PMU) measurements at all buses in a power system. The classifier is based on a novel combination of Graph Attention Networks and Long Short-Term memories, and is trained to label power system data in the form of captured windows of PMU measurements. These labels are then used to provide early warning for transient instability. The classifier is trained and tested data from simulations of the Nordic44 test system, and includes extensive topological variations under two different load levels. It is found that accurate early warnings can be provided, but the quality of prediction is highly dependent on specific power system characteristics, such as how quickly the power system responds to transient disturbances.