This study adapts the highly-versatile siamese neural network model to the event data domain. We introduce a supervised training framework for optimizing Earth Mover's Distance (EMD) between spike trains with spiking neural networks (SNN). We train this model on images of the MNIST dataset converted into spiking domain with novel conversion schemes. The quality of the siamese embeddings of input images was evaluated by measuring the classifier performance for different dataset coding types. The models achieved performance similar to existing SNN-based approaches (F1-score of up to 0.9386) while using only about 15% of hidden layer neurons to classify each example. Furthermore, models which did not employ a sparse neural code were about 45% slower than their sparse counterparts. These properties make the model suitable for low energy consumption and low prediction latency applications.