In the age of the data deluge there are still many domains and applications restricted to the use of small datasets. The ability to harness these small datasets to solve problems through the use of supervised learning methods can have a significant impact in many important areas. The insufficient size of training data usually results in unsatisfactory performance of machine learning algorithms. The current research work aims to contribute to mitigate the small data problem through the creation of artificial instances, which are added to the training process. The proposed algorithm, Geometric Small Data Oversampling Technique, uses geometric regions around existing samples to generate new high quality instances. Experimental results show a significant improvement in accuracy when compared with the use of the initial small dataset as well as other popular artificial data generation techniques.