Signed Diverse Multiplex Networks: Clustering and Inference
This work addresses the analysis of complex networks, such as brain networks, by providing a flexible model that improves estimation and clustering precision, though it is incremental as it builds on existing GRDPG frameworks.
The paper tackles the problem of clustering and inference in signed multiplex networks by introducing the Signed Generalized Random Dot Product Graph (SGRDPG) model, achieving strongly consistent clustering and highly accurate subspace estimation with significant improvements over prior work.
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, including GRDPG, as its particular cases. By employing novel methodologies, our paper ensures strongly consistent clustering of layers and highly accurate subspace estimation, which are significant improvements over the results of Pensky and Wang (2024). All algorithms and theoretical results in the paper remain true for both signed and binary networks. In addition, the paper 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.