Rank-adaptive Learning over Distributed Low-rank Networks via Online HQS Algorithm

Determining an accurate rank is essential for parameter estimation in low-rank distributed networks. To address this challenge, this paper proposes a rank-adaptive learning algorithm that ensures the estimated local matrices match the true rank. Given a strongly convex cost function at each node in the network, matrix factorization is firstly employed to formulate the optimization problem, decomposing a matrix into the product of two low-rank matrices to maintain a potentially low-rank structure. To promote row sparsity, a weighted sparse norm is imposed on one of the factorized matrices as a regularization term. Since the choice of weights critically affects rank estimation, an adaptive strategy is introduced to set weights. The local optimization problem is then solved using the half-quadratic splitting (HQS) algorithm. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.