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 all 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 analysis of
brain networks. Second, by employing novel algorithms, our paper ensures
equivalent or superior accuracy than has been achieved in simpler multiplex
network models. In addition to theoretical guarantees, both of those features
are demonstrated using numerical simulations and a real data example.

该论文引入了一种有符号广义随机点积图 (SGRDPG) 模型，通过保留网络构建过程中边的符号，实现了更好的估计和聚类精度，适用于解决现实世界问题，如大脑网络分析。同时，通过采用新算法，论文确保等价或优于简单多层网络模型的准确性，理论保证与数值模拟和真实数据实例的验证。