  In existing models and embedding methods of networked systems, node features
describing their qualities are usually overlooked in favor of focusing solely
on node connectivity. This study introduces $FiD$-Mercator, a model-based
ultra-low dimensional reduction technique that integrates node features with
network structure to create $D$-dimensional maps of complex networks in a
hyperbolic space. This embedding method efficiently uses features as an initial
condition, guiding the search of nodes' coordinates towards an optimal
solution. The research reveals that downstream task performance improves with
the correlation between network connectivity and features, emphasizing the
importance of such correlation for enhancing the description and predictability
of real networks. Simultaneously, hyperbolic embedding's ability to reproduce
local network properties remains unaffected by the inclusion of features. The
findings highlight the necessity for developing network embedding techniques
capable of exploiting such correlations to optimize both network structure and
feature association jointly in the future.
