This paper focuses on graph-level representation learning that aims to represent graphs as vectors that can be directly utilized in downstream tasks such as graph classification. We propose a novel graph-level representation learning principle called Lovász principle, which is motivated by the Lovász number in graph theory. The Lovász number of a graph is a real number that is an upper bound for graph Shannon capacity and is strongly connected with various global characteristics of the graph. Specifically, we show that the handle vector for computing the Lovász number is potentially a suitable choice for graph representation, as it captures a graph's global properties, though a direct application of the handle vector is difficult and problematic. We propose to use neural networks to address the problems and hence provide the Lovász principle. Moreover, we propose an enhanced Lovász principle that is able to exploit the subgraph Lovász numbers directly and efficiently. The experiments demonstrate that our Lovász principles achieve competitive performance compared to the baselines in unsupervised and semi-supervised graph-level representation learning tasks. The code of our Lovász principles is publicly available on GitHub.

This paper focuses on graph-level representation learning that aims to represent graphs as vectors that can be directly utilized in downstream tasks such as graph classification. We propose a novel graph-level representation learning principle called Lovász principle, which is motivated by the Lovász number in graph theory. The Lovász number of a graph is a real number that is an upper bound for graph Shannon capacity and is strongly connected with various global characteristics of the graph. Specifically, we show that the handle vector for computing the Lovász number is potentially a suitable choice for graph representation, as it captures a graph's global properties, though a direct application of the handle vector is difficult and problematic. We propose to use neural networks to address the problems and hence provide the Lovász principle. Moreover, we propose an enhanced Lovász principle that is able to exploit the subgraph Lovász numbers directly and efficiently.

Research in machine learning for autism spectrum disorder (ASD) classification bears the promise to improve clinical diagnoses. However, recent studies in clinical imaging have shown the limited generalization of biomarkers across and beyond benchmark datasets. Despite increasing model complexity and sample size in neuroimaging, the classification performance of ASD remains far away from clinical application. This raises the question of how we can overcome these barriers to develop early biomarkers for ASD. One approach might be to rethink how we operationalize the theoretical basis of this disease in machine learning models. Here we introduced unsupervised graph representations that explicitly map the neural mechanisms of a core aspect of ASD, deficits in dyadic social interaction, as assessed by dual brain recordings, termed hyperscanning, and evaluated their predictive performance. The proposed method differs from existing approaches in that it is more suitable to capture social interaction deficits on a neural level and is applicable to young children and infants. First results from functional near-infrared spectroscopy data indicate potential predictive capacities of a task-agnostic, interpretable graph representation. This first effort to leverage interaction-related deficits on neural level to classify ASD may stimulate new approaches and methods to enhance existing models to achieve developmental ASD biomarkers in the future.