Progress in sensor technology leads to an ever-increasing amount of remote sensing data which needs to be classified in order to extract information. This big amount of data requires parallel processing by running parallel implementations of classification algorithms, such as Support Vector Machines (SVMs), on High-Performance Computing (HPC) clusters. Tomorrow's supercomputers will be able to provide exascale computing performance by using specialised hardware accelerators. However, existing software processing chains need to be adapted to make use of the best fitting accelerators. To address this problem, a mapping of an SVM remote sensing classification chain to the Dynamical Exascale Entry Platform (DEEP), a European pre-exascale platform, is presented. It will allow to scale SVM-based classifications on tomorrow's hardware towards exascale performance.