  Electronic systems living on Archimedean lattices such as kagome and
square-octagon networks are presently being intensively discussed for the
possible realization of topological insulating phases. Coining the most
interesting electronic topological states in an unbiased way is however not
straightforward due to the large parameter space of possible Hamiltonians. A
possible approach to tackle this problem is provided by a recently developed
statistical learning method [T. Mertz and R. Valent\'i, Phys. Rev. Research 3,
013132 (2021)], based on the analysis of a large data sets of randomized
tight-binding Hamiltonians labeled with a topological index. In this work, we
complement this technique by introducing a feature engineering approach which
helps identifying polynomial combinations of Hamiltonian parameters that are
associated with non-trivial topological states. As a showcase, we employ this
method to investigate the possible topological phases that can manifest on the
square-octagon lattice, focusing on the case in which the Fermi level of the
system lies at a high-order van Hove singularity, in analogy to recent studies
of topological phases on the kagome lattice at the van Hove filling.
