In this paper we propose a Kronecker-based modeling of large networks withunknown interconnection links. The class of Kronecker networks is defined forwhich we formulate a Vector Autoregressive model. Its coefficient-matrices aredecomposed into a sum of Kronecker products. When the network is labeled suchthat the number of terms in the sum is small compared to the size of thematrix, exploiting this Kronecker structure leads to high data compression. Twoalgorithms were designed for an efficient estimation of thecoefficient-matrices, namely a non-iterative and overparametrized algorithm aswell as an Alternating Least Squares minimization. We prove that the latteralways converges to the true parameters for non-zero initial conditions. Thisframework moreover allows for a convenient integration of more structure (e.gsparse, banded, Toeplitz) on smaller-size matrices. Numerical examples onatmospheric turbulence data has shown comparable performances with theunstructured least-squares estimation while the number of parameters is growingonly linearly w.r.t. the number of nodes instead of quadratically in the fullunstructured matrix case.
展开▼
