Online Distributed ADMM Algorithm With RLS-Based Multitask Graph Filter Models

This article establishes a multitask graph filter model based on the recursive least square (RLS) method and proposes an online distributed alternating direction method of multipliers (ODADMM) algorithm. We are interested in the time-varying graph signal, i.e., the graph filter is estimated from streaming data. Considering that current popular graph shift operators' energy can not be preserved, which will lead to slow estimation speed, so the RLS method is adopted in graph filters (GFs) to improve the convergence rate. Besides, a multitask GFs model is proposed for node-variant GFs, where each vertex cooperates with neighbours to improve the estimation performance by utilizing the correlation of tasks. Then, according to our model, a distributed alternating direction method of multipliers (DADMM) algorithm is designed, while it has enormous computational complexity. To address this drawback, an ODADMM algorithm is further developed, and the algorithm can converge to an optimal point that is validated. Numerical results verify that the proposed algorithm is more competitive in convergence speed and performance than other related algorithms, and two real scenes are tested to verify the effectiveness of the algorithm.