Online Distributed Learning Over Graphs With Multitask GraphFilter Models In this article, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graphshift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an illconditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and meansquare sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results.

Graph Filtering with Quantization over Random Timevarying Graphs Distributed graph filters can be implemented over wireless sensor networks by means of cooperation and exchanges among nodes. However, in practice, the performance of such graph filters is deeply affected by the quantization errors that are accumulated when the messages are transmitted. The latter is paramount to overcome the limitations in terms of bandwidth and computation capabilities in sensor nodes. In addition to quantization errors, distributed graph filters are also affected by random packet losses due to interferences and background noise, leading to the degradation of the performance in terms of the filtering accuracy. In this work, we consider the problem of designing graph filters that are robust to quantized data and timevarying topologies. We propose an optimized method that minimizes the quantization error, while ensuring an accurate filtering over timevarying graph topologies. The efficiency of the proposed theoretical findings is validated by numerical results in random wireless sensor networks.