Relations between chemical composition, the spatial arrangement of atoms (structure) and the evolving macroscopic properties are of central interest in glass science and technology . The concentration of a single chemical element (or nominal compound) is the intuitive descriptor for starting to explore these relations. However, this simplistic approach is usually insufficient to account for material behaviour in glasses containing multiple chemical elements, in particular, for properties as complex as ionic conductivity . A plot of a material property over the concentration of a single element may show, in this case, broadly scattered data, a vertical line, or some kind of mathematical trend with more or less outliers, all of which can be highly misleading. Instead, such observations might be caused by insufficient expressivity when using single-component concentration values as descriptors: multi-component glasses usually exhibit intricate, typically unknown non-linear relationships and interdependencies involving multiple elemental species. From this, the immediate question arises as to how multi-component descriptors can be identified for a given glass property, i.e., the glass genome . Are all or only some of the elements forming the material involved in individual such descriptors? What is the molar ratio of each element in these descriptor constructions? Can the descriptors be traced back -directly or indirectly -to structural entities or building blocks known to exist in the material? In the following, we will demonstrate how these questions can be answered through analyzing compostion -property correlations for strong linear components, introducing Strong Linear Component Analysis (SLCA) for deciphering glass property genomes on small datasets.