Graph embedding into vector spaces is a widely used practice in graph-based pattern recognition to bypass the mathematical limitations of the graph domain. Several methods for graph embedding have been proposed in the last decades. Many of them are based on graph kernels which produce implicit embeddings that are sometimes hard to interpret. There are also explicit graph embeddings available that produce more interpretable results. However, these methods are often computationally expensive. In the present paper, we propose an approach that combines Graph Attention Networks (GAT) and Dissimilarity Based Graph Embedding (DBGE) for the first time. The major goal of our novel method is to produce DBGEs with much smaller computation time than with the original method. To achieve this goal, we train a GAT to learn embeddings from a dissimilarity matrix previously calculated on training data. In an empirical evaluation on four graphs datasets, we observe a considerable time reduction compared to the original embedding technique without any noticeable deterioration in classification performance.