  Percolation is an emblematic model to assess the robustness of interconnected
systems when some of their components are corrupted. It is usually investigated
in simple scenarios, such as the removal of the system's units in random order,
or sequentially ordered by specific topological descriptors. However, in the
vast majority of empirical applications, it is required to dismantle the
network following more sophisticated protocols, for instance, by combining
topological properties and non-topological node metadata. We propose a novel
mathematical framework to fill this gap: networks are enriched with features
and their nodes are removed according to the importance in the feature space.
We consider features of different nature, from ones related to the network
construction to ones related to dynamical processes such as epidemic spreading.
Our framework not only provides a natural generalization of percolation but,
more importantly, offers an accurate way to test the robustness of networks in
realistic scenarios.
