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Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis ; ; Alves Martins, Wallace et al in IEEE Transactions on Signal and Information Processing over Networks (2020) This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters ... [more ▼] This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters that operate on graph-shifted versions of the input signal. We then propose a centralized graph kernel least mean squares (GKLMS) algorithm to identify nonlinear graph filters' model parameters. To reduce the dictionary size of the centralized GKLMS, we apply the principles of coherence check and random Fourier features (RFF). The resulting algorithms have performance close to that of the GKLMS algorithm. Additionally, we leverage the graph structure to derive the distributed graph diffusion KLMS (GDKLMS) algorithms. We show that, unlike the coherence check-based approach, the GDKLMS based on RFF avoids the use of a pre-trained dictionary through its data independent fixed structure. We conduct a detailed performance study of the proposed RFF-based GDKLMS, and the conditions for its convergence both in mean and mean-squared senses are derived. Extensive numerical simulations show that GKLMS and GDKLMS can successfully identify nonlinear graph filters and adapt to model changes. Furthermore, RFF-based strategies show faster convergence for model identification and exhibit better tracking performance in model-changing scenarios. [less ▲] Detailed reference viewed: 23 (1 UL)Joint Forecasting and Interpolation of Time-Varying Graph Signals Using Deep Learning ; Alves Martins, Wallace ; Chatzinotas, Symeon et al in IEEE Transactions on Signal and Information Processing over Networks (2020) We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series ... [more ▼] We tackle the problem of forecasting network-signal snapshots using past signal measurements acquired by a subset of network nodes. This task can be seen as a combination of multivariate time-series forecasting (temporal prediction) and graph signal interpolation (spatial prediction). This is a fundamental problem for many applications wherein deploying a high granularity network is impractical. Our solution combines recurrent neural networks with frequency-analysis tools from graph signal processing, and assumes that data is sufficiently smooth with respect to the underlying graph. The proposed learning model outperforms state-of-the-art deep learning techniques, especially when predictions are made using a small subset of network nodes, considering two distinct real world datasets: temperatures in the US and speed flow in Seattle. The results also indicate that our method can handle noisy signals and missing data, making it suitable to many practical applications. [less ▲] Detailed reference viewed: 37 (3 UL)Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances ; Alves Martins, Wallace ; in IEEE Transactions on Signal and Information Processing over Networks (2020) This paper proposes the augmentation of the adjacency model of networks for graph signal processing. It is assumed that no information about the network is available, apart from the initial adjacency ... [more ▼] This paper proposes the augmentation of the adjacency model of networks for graph signal processing. It is assumed that no information about the network is available, apart from the initial adjacency matrix. In the proposed model, additional edges are created according to a Markov relation imposed between nodes. This information is incorporated into the extended-adjacency matrix as a function of the diffusion distance between nodes. The diffusion distance measures similarities between nodes at a certain diffusion scale or time, and is a metric adopted from diffusion maps. Similarly, the proposed extended-adjacency matrix depends on the diffusion scale, which enables the definition of a scale-dependent graph Fourier transform. We conduct theoretical analyses of both the extended adjacency and the corresponding graph Fourier transform and show that different diffusion scales lead to different graph-frequency perspectives. At different scales, the transform discriminates shifted ranges of signal variations across the graph, revealing more information on the graph signal when compared to traditional approaches. The scale-dependent graph Fourier transform is applied for anomaly detection and is shown to outperform the conventional graph Fourier transform. [less ▲] Detailed reference viewed: 153 (7 UL)An online parallel algorithm for recursive estimation of sparse signals Yang, Yang ; ; et al in IEEE Transactions on Signal and Information Processing over Networks (2016), 2(3), 290-305 Detailed reference viewed: 192 (5 UL) |
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