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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
This work presents a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs.
Fast Global Minimization of the Active Contour/Snake Model
- X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran, S. Osher
- Computer ScienceJournal of Mathematical Imaging and Vision
- 1 June 2007
This paper proposes to unify three well-known image variational models, namely the snake model, the Rudin–Osher–Fatemi denoising model and the Mumford–Shah segmentation model, and establishes theorems with proofs to determine a global minimum of the active contour model.
Benchmarking Graph Neural Networks
- Vijay Prakash Dwivedi, Chaitanya K. Joshi, T. Laurent, Yoshua Bengio, X. Bresson
- Computer ScienceArXiv
A reproducible GNN benchmarking framework is introduced, with the facility for researchers to add new models conveniently for arbitrary datasets, and a principled investigation into the recent Weisfeiler-Lehman GNNs (WL-GNNs) compared to message passing-based graph convolutional networks (GCNs).
Fast dual minimization of the vectorial total variation norm and applications to color image processing
We propose a regularization algorithm for color/vectorial images which is fast, easy to code and mathematically well-posed. More precisely, the regularization model is based on the dual formulation…
Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks
This paper proposes a novel approach to overcome limitations of matrix completion techniques by using geometric deep learning on graphs, and applies this method on both synthetic and real datasets, showing that it outperforms state-of-the-art techniques.
Structured Sequence Modeling with Graph Convolutional Recurrent Networks
The proposed model combines convolutional neural networks on graphs to identify spatial structures and RNN to find dynamic patterns in data structured by an arbitrary graph.
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
The proposed general algorithm framework for inverse problem regularization with a single forward-backward operator step, namely, Bregmanized operator splitting (BOS), converges without fully solving the subproblems, and numerical results on deconvolution and compressive sensing illustrate the performance of nonlocal total variation regularization under the proposed algorithm framework.
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
The primary purpose of this paper is to examine the effectiveness of “Split Bregman” techniques for solving image segmentation problems, and to compare this scheme with more conventional methods.
An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem
This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP…
Residual Gated Graph ConvNets
This work reviews existing graph RNN and ConvNet architectures, and proposes natural extension of LSTM and Conv net to graphs with arbitrary size, and designs a set of analytically controlled experiments on two basic graph problems to test the different architectures.