Extended Adjacency and Scale-dependent Graph Fourier Transform via Diffusion Distances

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 ▲]

Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis

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 ▲]

Intersymbol and Intercarrier Interference in OFDM Transmissions Through Highly Dispersive Channels

in Proc. of the 27th European Signal Processing Conference (EUSIPCO-2019) (2019, September)

On the Use of Vertex-Frequency Analysis for Anomaly Detection in Graph Signals

in Anais do XXXVII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT 2019) (2019, September)

Convex Combination of Constraint Vectors for Set-membership Affine Projection Algorithms

in Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2019, May)

Set-membership affine projection (SM-AP) adaptive filters have been increasingly employed in the context of online data-selective learning. A key aspect for their good performance in terms of both ... [more ▼]

Set-membership affine projection (SM-AP) adaptive filters have been increasingly employed in the context of online data-selective learning. A key aspect for their good performance in terms of both convergence speed and steady-state mean-squared error is the choice of the so-called constraint vector. Optimal constraint vectors were recently proposed relying on convex optimization tools, which might some- times lead to prohibitive computational burden. This paper proposes a convex combination of simpler constraint vectors whose performance approaches the optimal solution closely, utilizing much fewer computations. Some illustrative examples confirm that the sub-optimal solution follows the accomplishments of the optimal one. [less ▲]

Normalized LMS Algorithm and Data-selective Strategies for Adaptive Graph Signal Estimation

in Signal Processing (2019)

This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive ... [more ▼]

This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive filtering framework, the resulting GS estimation technique converges faster than the least-mean-squares (LMS) algorithm while being less complex than the recursive least-squares (RLS) algorithm, both recently recast as adaptive estimation strategies for the GS framework. Detailed steady-state mean-squared error and deviation analyses are provided for the proposed NLMS algorithm, and are also employed to complement previous analyses on the LMS and RLS algorithms. Additionally, two different time-domain data-selective (DS) strategies are proposed to reduce the overall computational complexity by only performing updates when the input signal brings enough innovation. The parameter setting of the algorithms is performed based on the analysis of these DS strategies, and closed formulas are derived for an accurate evaluation of the update probability when using different adaptive algorithms. The theoretical results predicted in this work are corroborated with high accuracy by numerical simulations. [less ▲]