8 research outputs found
Deep Learning-Based Average Consensus
In this study, we analyzed the problem of accelerating the linear average
consensus algorithm for complex networks. We propose a data-driven approach to
tuning the weights of temporal (i.e., time-varying) networks using deep
learning techniques. Given a finite-time window, the proposed approach first
unfolds the linear average consensus protocol to obtain a feedforward
signal-flow graph, which is regarded as a neural network. The edge weights of
the obtained neural network are then trained using standard deep learning
techniques to minimize consensus error over a given finite-time window. Through
this training process, we obtain a set of optimized time-varying weights, which
yield faster consensus for a complex network. We also demonstrate that the
proposed approach can be extended for infinite-time window problems. Numerical
experiments revealed that our approach can achieve a significantly smaller
consensus error compared to baseline strategies
Hubs-attracting laplacian and related synchronization on networks
In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher probability from low to high degree nodes. This notion complements the one of the hubs-repelling Laplacian discussed in [E. Estrada, Linear Algebra Appl., 596 (2020), pp. 256-280], that considers the opposite scenario, with higher hopping probabilities from high to low degree nodes. We formulate a model of oscillators coupled through the new Laplacian and study the synchronizability of the network through the analysis of the spectrum of the Laplacian. We discuss analytical results providing bounds for the quantities of interest for synchronization and computational results showing that the hubs-attracting Laplacian generally has better synchronizability properties when compared to the classical one, with a low occurrence rate for the graphs where this is not true. Finally, two illustrative case studies of synchronization through the hubs-attracting Laplacian are considered