An Underparametrized Deep Decoder Architecture for Graph Signals

Abstract

While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform state-of-the-art methods in several tasks such as image compression and denoising. Motivated by the fact that many contemporary datasets have an irregular structure different from a 1D/2D grid, this paper generalizes untrained and underparametrized non-convolutional architectures to signals defined over irregular domains represented by graphs. The proposed architecture consists of a succession of layers, each of them implementing an upsampling operator, a linear feature combination, and a scalar nonlinearity. A novel element is the incorporation of upsampling operators accounting for the structure of the supporting graph, which is achieved by considering a systematic graph coarsening approach based on hierarchical clustering. The numerical results carried out in synthetic and real-world datasets showcase that the reconstruction performance can improve drastically if the information of the supporting graph topology is taken into account.

Untrained Graph Neural Networks for Denoising

“…The GCG architecture presented in Section IV incorporated the topology of G via the vertex-based convolutions implemented by the graph filter H with S = Ã. In this section, we introduce the graph decoder (GD) 2 architecture, a new graph-aware denoising NN that incorporates the topology of G via a (nested) collection of graph upsampling operators [48]. Specifically, we propose the linear transformation for the GD denoiser to be given by…”

A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters

“…The goal in graph-signal denoising is to recover the original graph signal x ∈ R N given the noisy graph-signal observation y = x + w, with w ∈ R N representing a noise vector. To that end, we approach the denoising problem as in [17], [30] by minimizing…”

Generative Adversarial Networks for Graph Data Imputation from Signed Observations

“…where the scalars α and β control the trade-off between the different components of the loss function at the generator. As typically done, we optimize (10) in an iterative manner where we first fix θ and update the parameters of the discriminator via mini-batch training, followed by fixing ψ and updating the values of θ accordingly. More details on the implementation and hyperparameter selection are given in the next section.…”

“…A broad range of graph signals exist, with meaningful examples including neural activity defined on the regions of a brain network, the spread of a rumor on a social network, and the delay experienced at each station of a subway network. In recent years, the processing of graph signals has attracted a lot of attention from the statistics, machine learning (ML), and signal processing (SP) communities, with relevant results including sampling and inpainting [1][2][3][4][5][6][7], denoising [8][9][10], filtering [11,12], and deep graph convolutional architectures [13][14][15] for graph supported data.…”