References of "Werner, Stefan"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailDiffusion-based Virtual Graph Adjacency for Fourier Analysis of Network Signals
Elias, Vitor R. M.; Alves Martins, Wallace UL; Werner, Stefan

in XXXVIII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES E PROCESSAMENTO DE SINAIS, Florianópolis 22-25 November 2020 (2020, November)

This work proposes a graph model for networks where node collaborations can be described by the Markov property. The proposed model augments an initial graph adjacency using diffusion distances. The ... [more ▼]

This work proposes a graph model for networks where node collaborations can be described by the Markov property. The proposed model augments an initial graph adjacency using diffusion distances. The resulting virtual adjacency depends on a diffusion-scale parameter, which leads to a controlled shift in the graph-Fourier-transform spectrum. This enables a frequency analysis tailored to the actual network collaboration, revealing more information on the graph signal when compared to traditional approaches. The proposed model is employed for anomaly detection in real and synthetic networks, and results confirm that using the proposed virtual adjacency yields better classification than the initial adjacency. [less ▲]

Detailed reference viewed: 68 (3 UL)
Full Text
Peer Reviewed
See detailGraph Diffusion Kernel LMS using Random Fourier Features
Gogineni, Vinay; Elias, Vitor R. M.; Alves Martins, Wallace UL et al

in 2020 54th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 1-5 November 2020 (2020, November)

This work introduces kernel adaptive graph filters that operate in the reproducing kernel Hilbert space. We propose a centralized graph kernel least mean squares (GKLMS) approach for identifying the ... [more ▼]

This work introduces kernel adaptive graph filters that operate in the reproducing kernel Hilbert space. We propose a centralized graph kernel least mean squares (GKLMS) approach for identifying the nonlinear graph filters. The principles of coherence-check and random Fourier features (RFF) are used to reduce the dictionary size. Additionally, we leverage on the graph structure to derive the graph diffusion KLMS (GDKLMS). The proposed GDKLMS requires only single-hop communication during successive time instants, making it viable for real-time network-based applications. In the distributed implementation, usage of RFF avoids the requirement of a centralized pretrained dictionary in the case of coherence-check. Finally, the performance of the proposed algorithms is demonstrated in modeling a nonlinear graph filter via numerical examples. The results show that centralized and distributed implementations effectively model the nonlinear graph filters, whereas the random feature-based solutions is shown to outperform coherence-check based solutions. [less ▲]

Detailed reference viewed: 70 (4 UL)
Full Text
Peer Reviewed
See detailAdaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis
Elias, Vitor R. M.; Gogineni, Vinay C.; Alves Martins, Wallace UL 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)
Full Text
Peer Reviewed
See detailExtended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances
Elias, Vitor R.M.; Alves Martins, Wallace UL; Werner, Stefan

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)