Context. With the rise of integral field spectroscopy (IFS), we are currently dealing with large amounts of spatially resolved data, whose analysis has become challenging, especially when observing complex objects such as nearby galaxies. Aims. We aim to develop a method of automatically separating regions with different physical properties (ionisation, kinematics, etc.) within the central parts (1″ ∼ 160 pc, on average) of galaxies. This could allow us to better understand the systems and provide an initial characterisation of the main ionisation sources affecting its evolution. Methods. We developed an unsupervised hierarchical clustering algorithm to analyse data cubes based on spectral similarity. It clusters spaxels together with similar spectra, which is useful to disentangle regions affected by different processes, such as ionisation sources. We applied this method to a sample of 15 nearby (distances < 100 Mpc) galaxies: 7 from the Galaxy Activity, Torus, and Outflow Survey (GATOS) and 8 archival sources, all observed with the medium-resolution spectrometer (MRS) of the Mid-Infrared Instrument (MIRI) on board the James Webb Space Telescope (JWST). The sample spans sources of various morphologies, active galactic nucleus (AGN) types, and/or starbursts. From the clusters, we computed their median spectrum and measured the line and continuum properties. We used these measurements to train random forest models and create several empirical mid-IR diagnostic diagrams for the MRS channel 3 wavelength range, ranging from 11.5 to 18 μm, which includes among others the bright [Ne II], [Ne III], and [Ne V] lines, several H2 transitions, and PAH features. Results. The clustering technique allows one to differentiate emission coming from an AGN, a nuclear starburst, the disc and star-forming (SF) regions in the galaxies, and other composite regions, potentially ionised by several sources simultaneously. This is supported by the results from the empirical diagnostic diagrams, which are indeed able to separate physically distinct regions. This innovative method serves as a tool to identify regions of interest in any data cube prior to an in-depth analysis of the sources. In a future work, we shall explore other wavelength ranges and a larger sample that would help us to obtain statistically significant conclusions.