Functional-Edged Network Modeling
Haijie Xu Chen Zhang
Contrasts with existing works which all consider nodes as functions and use
edges to represent the relationships between different functions. We target at
network modeling whose edges are functional data and transform the adjacency
matrix into a functional adjacency tensor, introducing an additional dimension
dedicated to function representation. Tucker functional decomposition is used
for the functional adjacency tensor, and to further consider the community
between nodes, we regularize the basis matrices to be symmetrical. Furthermore,
to deal with irregular observations of the functional edges, we conduct model
inference to solve a tensor completion problem. It is optimized by a Riemann
conjugate gradient descent method. Besides these, we also derive several
theorems to show the desirable properties of the functional edged network
model. Finally, we evaluate the efficacy of our proposed model using simulation
data and real metro system data from Hong Kong and Singapore.