  The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG)
model, which is a variant of the Generalized Random Dot Product Graph (GRDPG),
where, in addition, edges can be positive or negative. The setting is extended
to a multiplex version, where all layers have the same collection of nodes and
follow the SGRDPG. The only common feature of the layers of the network is that
they can be partitioned into groups with common subspace structures, while
otherwise matrices of connection probabilities can be all different. The
setting above is extremely flexible and includes a variety of existing
multiplex network models as its particular cases. The paper fulfills two
objectives. First, it shows that keeping signs of the edges in the process of
network construction leads to a better precision of estimation and clustering
and, hence, is beneficial for tackling real world problems such as, for
example, analysis of brain networks. Second, by employing novel algorithms, our
paper ensures strongly consistent clustering of layers and high accuracy of
subspace estimation. In addition to theoretical guarantees, both of those
features are demonstrated using numerical simulations and a real data example.
