A fundamental bimodality of galaxies in the local Universe is apparent in many of the features used to describe them. Multiple sub-populations exist within this framework, each representing galaxies following distinct evolutionary pathways. Accurately identifying and characterizing these sub-populations requires that a large number of galaxy features be analysed simultaneously. Future galaxy surveys such as LSST and Euclid will yield data volumes for which traditional approaches to galaxy classification will become unfeasible. To address this, we apply a robust k-means unsupervized clustering method to feature data derived from a sample of 7338 local-Universe galaxies selected from the Galaxy And Mass Assembly (GAMA) survey. This allows us to partition our sample into k clusters without the need for training on pre-labelled data, facilitating a full census of our high-dimensionality feature space and guarding against stochastic effects. We find that the local galaxy population natively splits into 2, 3, 5, and a maximum of six sub-populations, with each corresponding to a distinct ongoing evolutionary mechanism. Notably, the impact of the local environment appears strongly linked with the evolution of low-mass (M* < 1010 M☉) galaxies, with more massive systems appearing to evolve more passively from the blue cloud on to the red sequence. With a typical run time of ̃3 min per value of k for our galaxy sample, we show how k-means unsupervized clustering is an ideal tool for future analysis of large extragalactic data sets, being scalable, adaptable, and providing crucial insight into the fundamental properties of the local galaxy population....