Functional-Edged Network Modeling

We study a novel class of networks, referred to as functional-edged networks, where the weight of each edge is represented as a smooth function over time rather than a scalar or vector. To model such networks, we introduce a functional adjacency tensor that extends the conventional adjacency matrix by incorporating a continuous functional dimension for edge representation. To analyze the structural patterns within this functional adjacency tensor, we propose a novel functional Tucker decomposition framework. To further capture potential community structures among nodes, we impose symmetry regularization on the basis matrices derived from the decomposition. In addition, to handle the challenge of irregular observations across functional edges, we formulate the model inference as a tensor completion problem, and solve it using a Riemannian conjugate gradient method. We establish the theoretical properties of the proposed model and validate its effectiveness through extensive experiments on both synthetic datasets and real-world metro system data from Hong Kong and the received signal strength indicator data from an industrial IoT system.