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

Elias, Vitor R. M.; Gogineni, Vinay Chakravarthi; Martins, Wallace A.; Werner, Stefan

doi:10.1109/tsipn.2020.3046217

Cited by 24 publications

(11 citation statements)

References 63 publications

(91 reference statements)

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“…By taking the limit of the expected absolute value of (22) as k → ∞ and using the same approximation for R p and R w in Section 4.1 , the spectral domain absolute error update can be expressed as…”

Section: Mean-absolute Deviations Stability Analysis Under Steady-sta...mentioning

confidence: 99%

“…Recent attention has focused on the distributed version of GSP algorithms [19,20] which merge the distributed GLMS algorithm with diffusion algorithms and [21] gives a distributed version of the GRLS algorithm. Similarly, distributed kernel GLMS was introduced in [22] which extended the linear graph adaptive algorithm to a nonlinear version. Recent studies have applied classical time-series analysis techniques, such as the ARMA models, to GSP [23] .…”

Section: Introductionmentioning

confidence: 99%

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Adaptive sign algorithm for graph signal processing

2022

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Section: Mean-absolute Deviations Stability Analysis Under Steady-sta...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive sign algorithm for graph signal processing

2022

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“…Then we can build Our analysis framework can be helpful for other algorithms which have a (shift-invariant-)kernel-based learning model. For example, GKLMS-RFF in [20] has the same learning model, but uses filtered nodal value time series by a known graph filter as the model input. Our analysis can explicitly point out how to configure the model in the GKLMS-RFF algorithm.…”

Section: Extension Of the Analysismentioning

confidence: 99%

“…Among many kinds of shift-invariant kernels [15], e.g., Gaussian kernels, Laplacian kernels, and Cauchy kernels, we will focus on Gaussian kernels. Noting that the kernel being used models how similarity changes with difference, and that the laws of large numbers indicate wide application of the Gaussian distribution, it is intuitive to use Gaussian kernels in most situations [16], [17], [20]. For this reason, in this paper we will discuss SKG with a Gaussian kernel in detail.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphs

Zhao,

Ayanoglu

2022

Preprint

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This paper discusses a special kind of a simple yet possibly powerful algorithm, called single-kernel Gradraker (SKG), which is an adaptive learning method predicting unknown nodal values in a network using known nodal values and the network structure. We aim to find out how to configure the special kind of the model in applying the algorithm. To be more specific, we focus on SKG with a Gaussian kernel and specify how to find a suitable variance for the kernel. To do so, we introduce two variables with which we are able to set up requirements on the variance of the Gaussian kernel to achieve (near-) optimal performance and can better understand how SKG works.Our contribution is that we introduce two variables as analysis tools, illustrate how predictions will be affected under different Gaussian kernels, and provide an algorithm finding a suitable Gaussian kernel for SKG with knowledge about the training network. Simulation results on real datasets are provided.

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“…Typically, state-of-the-art techniques address the case where both reference and target signals share the same graph. In the context of linear system modeling, different learning problems have been studied within the GSP framework, e.g., classification on graphs [19], autoregressive models for graph signal prediction [15], [16], [20], dictionary learning [21], and distributed adaptive filtering [8]- [14]. Several learning strategies have been proposed for the nonlinear setting as well.…”

Section: Introductionmentioning

confidence: 99%

Kernel Regression Over Graphs Using Random Fourier Features

Elias

Gogineni

Martins

et al. 2022

IEEE Trans. Signal Process.

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This paper proposes efficient batch-based and online strategies for kernel regression over graphs (KRG). The proposed algorithms do not require the input signal to be a graph signal, whereas the target signal is defined over the graph. We first use random Fourier features (RFF) to tackle the complexity issues associated with kernel methods employed in the conventional KRG. For batch-based approaches, we also propose an implementation that reduces complexity by avoiding the inversion of large matrices. Then, we derive two distinct online strategies using RFF, namely, the mini-batch gradient KRG (MGKRG) and the recursive least squares KRG (RLSKRG). The stochasticgradient KRG (SGKRG) is introduced as a particular case of the MGKRG. The MGKRG and the SGKRG are low-complexity algorithms that employ stochastic gradient approximations in the regression-parameter update. The RLSKRG is a recursive implementation of the RFF-based batch KRG. A detailed stability analysis is provided for the proposed online algorithms, including convergence conditions in both mean and mean-squared senses. A discussion on complexity is also provided. Numerical simulations include a synthesized-data experiment and real-data experiments on temperature prediction, brain activity estimation, and image reconstruction. Results show that the RFF-based batch implementation offers competitive performance with a reduced computational burden when compared to the conventional KRG. The MGKRG offers a convenient trade-off between performance and complexity by varying the number of mini-batch samples. The RLSKRG has a faster convergence than the MGKRG and matches the performance of the batch implementation.

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

Cited by 24 publications

References 63 publications

Adaptive sign algorithm for graph signal processing

Adaptive sign algorithm for graph signal processing

Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphs

Kernel Regression Over Graphs Using Random Fourier Features

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