🤖 AI Summary
Clustering and inference in signed, heterogeneous multilayer networks remain challenging due to substantial inter-layer variation in edge probability matrices, despite underlying shared low-dimensional subspace structure.
Method: We propose the Signed Generalized Random Dot Product Graph (SGRDPG) and its multilinear extension, the first framework to systematically incorporate edge sign information into multilayer network embedding and subspace clustering. It enables joint estimation of a shared latent subspace and layer-consistent clustering.
Results: We establish theoretical consistency and asymptotic normality of the estimators. Extensive experiments on synthetic data and real human brain functional connectivity networks demonstrate that our method significantly outperforms sign-agnostic baselines: clustering accuracy and parameter estimation precision both improve markedly, validating the critical role of signed edge information in multilayer network analysis.
📝 Abstract
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.