In positron emission tomography (PET) studies, convolutional neural networks (CNNs) may be applied directly to the reconstructed distribution of radioactive tracers injected into the patient's body, as a pattern recognition tool. Nonetheless, unprocessed PET coincidence data exist in tabular format. This paper develops the transformation of tabular data into n-dimensional matrices, as a preparation stage for classification based on CNNs. This method explicitly introduces a nonlinear transformation at the feature engineering stage and then uses principal component analysis to create the images. We apply the proposed methodology to the classification of simulated PET coincidence events originating from NEMA IEC and anthropomorphic XCAT phantom. Comparative studies of neural network architectures, including multilayer perceptron and convolutional networks, were conducted. The developed method increased the initial number of features from 6 to 209 and gave the best precision results (79.8) for all tested neural network architectures; it also showed the smallest decrease when changing the test data to another phantom.