  A main goal of data-driven materials research is to find optimal
low-dimensional descriptors, allowing us to predict a physical property, and to
interpret them in a human-understandable way. In this work, we advance methods
to identify descriptors out of a large pool of candidate features by means of
compressed sensing. To this extent, we develop schemes for engineering
appropriate candidate features that are based on simple basic properties of
building blocks that constitute the materials and that are able to represent a
multi-component system by scalar numbers. Cross-validation based
feature-selection methods are developed for identifying the most relevant
features, thereby focusing on high generalizability. We apply our approaches to
an \textit{ab initio} dataset of ternary group-IV compounds to obtain a set of
descriptors for predicting lattice constants and energies of mixing. In
particular, we introduce simple complexity measures in terms of involved
algebraic operations as well as the amount of utilized basic properties.
