Graph-Based Semi-Supervised Segregated Lipschitz Learning

This paper presents an approach to semi-supervised learning for the classification of data using the Lipschitz Learning on graphs. We develop a graph-based semi-supervised learning framework that leverages the properties of the infinity Laplacian to propagate labels in a dataset where only a few samples are labeled. By extending the theory of spatial segregation from the Laplace operator to the infinity Laplace operator, both in continuum and discrete settings, our approach provides a robust method for dealing with class imbalance, a common challenge in machine learning. Experimental validation on several benchmark datasets demonstrates that our method not only improves classification accuracy compared to existing methods but also ensures efficient label propagation in scenarios with limited labeled data.

Variational models for signal processing with Graph Neural Networks

This paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets. While it is also the case for the processing of point-clouds with Graph Neural Networks (GNN), the focus has been largely given to high-level tasks such as classification and segmentation using supervised learning on labeled datasets such as ShapeNet. Yet, such datasets are scarce and time-consuming to build depending on the target application. In this work, we investigate the use of variational models for such GNN to process signals on graphs for unsupervised learning. Our contributions are two-fold. We first show that some existing variational-based algorithms for signals on graphs can be formulated as Message Passing Networks (MPN), a particular instance of GNN, making them computationally efficient in practice when compared to standard gradient-based machine learning algorithms. Secondly, we investigate the unsupervised learning of feed-forward GNN, either by direct optimization of an inverse problem or by model distillation from variational-based MPN. Keywords:Graph Processing. Neural Network. Total Variation. Variational Methods. Message Passing Network. Unsupervised learning