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.

翻译：本文提出了一种带符号广义随机点积图（SGRDPG）模型，该模型是广义随机点积图（GRDPG）的变体，其边可区分为正边或负边。该框架被扩展至多层版本，其中所有层共享相同的节点集合，并遵循SGRDPG模型。网络各层的唯一共同特征在于它们可被划分为具有共同子空间结构的组别，而除此之外，各层的连接概率矩阵可以完全互异。上述框架具有极高的灵活性，可将现有多种多层网络模型作为其特例纳入其中。本文实现两个目标：第一，证明在网络构建过程中保留边的符号信息能够提升估计与聚类的精度，因而有助于解决脑网络分析等现实问题；第二，通过采用新型算法，本文在精度上达到了与更简单的多层网络模型相当甚至更优的水平。除理论保证外，这两项优势均通过数值模拟和真实数据实例得到验证。