We present the first unsupervised classification of spaxels in hyperspectral images of individual galaxies. Classes identify regions by spectral similarity and thus take all the information into account that is contained in the data cubes (spatial and spectral). We used Gaussian mixture models in a latent discriminant subspace to find clusters of spaxels. The spectra were corrected for small-scale motions within the galaxy based on emission lines with an automatic algorithm. Our data consist of two MUSE/VLT data cubes of JKB 18 and NGC 1068 and one NIRSpec/JWST data cube of NGC 4151. Our classes identify many regions that are most often easily interpreted. Most of the 11 classes that we find for JKB 18 are identified as photoionised by stars. Some of them are known HII regions, but we mapped them as extended, with gradients of ionisation intensities. One compact structure has not been reported before, and according to diagnostic diagrams, it might be a planetary nebula or a denser HII region. For NGC 1068, our 16 classes are of active galactic nucleus-type (AGN) or star-forming regions. Their spatial distribution corresponds perfectly to well-known structures such as spiral arms and a ring with giant molecular clouds. A subclassification in the nuclear region reveals several structures and gradients in the AGN spectra. Our unsupervised classification of the MUSE data of NGC 1068 helps visualise the complex interaction of the AGN and the jet with the interstellar medium in a single map. The centre of NGC 4151 is very complex, but our classes can easily be related to ionisation cones, the jet, or H2 emission. We find a new elongated structure that is ionised by the AGN along the N-S axis perpendicular to the jet direction. It is rotated counterclockwise with respect to the axis of the H2 emission. Our work shows that the unsupervised classification of spaxels takes full advantage of the richness of the information in the data cubes by presenting the spectral and spatial information in a combined and synthetic way.