Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation

HE online prediction of irregularly structured multivariate signals across both spatial and temporal dimensions of the graph signal, which may not be obtainable in reality, is vital in various real-life applications, including demanding the necessity of methods that require no prior weather prediction [1], brain connectivity analysis [2], [3], knowledge. Graph Neural Network (GNN) has extended the traffic flow monitoring [4], and smart grid system management spatial and spectral GSP techniques to time-invariant machine [5]. The signals gathered in real life are often noisy and have learning tasks, including node classification, link prediction, missing values. When representing the irregularly structured and image classification [20], [21], [22]. Different from the multi-dimensionality in the time-varying signals using graphs, GSP approaches, GNN methods such as Graph Convolutional three challenges need to be addressed to bridge the gap Neural Networks and Graph Attention Networks learn the filter between the online prediction of the time-varying signal and from the given data through backpropagation. Additionally, the the spatial representation in the form of graph topology: non-linear activations found in GNNs are capable of handling reconstructing missing data, denoising noisy observations, and non-linear relationships in the signals, enabling GNNs to solve capturing the time-variation.