In an era of highly complex machine learning methods that often are informative but not straightforward to interpret, Principal Component Analysis (PCA) offers a simple, easily interpretable approach. With no fitting parameters, it extracts the most salient statistical trends in data without the need for training sets. In this paper, we explore a large range of composite stellar population models defined for detailed analyses of galaxy spectra from surveys. Six of the most prominent spectral indices are targeted to visualize a PCA-based latent space created by the model data. The age--metallicity degeneracy is broken in the three-dimensional space spanned by the first three eigenvectors, but we emphasize that non-trivial combinations of all six absorption indices are needed for this. Moreover, the last eigenvector suggests an intriguing tug of war between two Balmer indices: H $\gamma _A$ and $\mathrm{ H}\,\delta _A$, that can help discern the presence of recent bursting behaviour, as it exploits the different behaviour of the two indices over time-scales $\sim$0.5--1 Gyr. Comparisons can be made between SDSS and LEGA-C galaxy spectra based on the latent space created by the models. This method, based on pure data, produces excellent results in agreement with standard SPS model-fitting techniques, allowing for the study of stellar populations in a variety of surveys or observational/synthetic data bases on solid ground.