Bridging Distinct Spaces in Graph-Based Machine Learning

Abstract

Graph-based machine learning, encompassing Graph Edit Distances (GEDs), Graph Kernels, and Graph Neural Networks (GNNs), offers extensive capabilities and exciting potential. While each model possesses unique strengths for graph challenges, interrelations between their underlying spaces remain under-explored. In this paper, we introduce a novel framework for bridging these distinct spaces via GED cost learning. A supervised metric learning approach serves as an instance of this framework, enabling space alignment through pairwise distances and the optimization of edit costs. Experiments reveal the framework's potential for enhancing varied tasks, including regression, classification, and graph generation, heralding new possibilities in these fields.

Theoretical insights on the pre-image resolution in machine learning

“…In this paper, we provide theoretical insights on the pre-image problem and its resolution. This problem has been known for about 20 years [33], and is still of great interest nowadays, as shown recently in many frameworks: when dealing with nonlinear dictionary learning [40,31] and matrix completion [17]; when dealing with structured input spaces, such as in interpretable time series analytics [36], graph edit distances [23,24], representation learning on graphs [10] and structured prediction [15]; generative machines including generative kernel PCA [29] and multiview generation [30].…”