The growing amount of data produced by simulations and observations of space physics processes encourages the use of methods rooted in machine learning for data analysis and physical discovery. We apply a clustering method based on self-organizing maps to fully kinetic simulations of plasmoid instability, with the aim of assessing their suitability as a reliable analysis tool for both simulated and observed data. We obtain clusters that map well, a posteriori, to our knowledge of the process; the clusters clearly identify the inflow region, the inner plasmoid region, the separatrices and regions associated with plasmoid merging. Self-organizing map-specific analysis tools, such as feature maps and the unified distance matrix, provide us with valuable insights into both the physics at work and specific spatial regions of interest. The method appears as a promising option for the analysis of data, both from simulations and from observations, and could also potentially be used to trigger the switch to different simulation models or resolution in coupled codes for space simulations.