Title: Distortion Regularization for Distance-Preserving Graph Embedding
Primary area: learning on graphs and other geometries & topologies
Keywords: vertex embedding, distance preservation, distortion, representation learning, Gaussian kernel

Abstract: Vertex embedding of graph-structured data offers the advantage of representing the graph in a low-dimensional continuous space, but it does not guarantee the preservation of distances. In this paper, we introduce a general distortion measure that can be integrated into loss functions. The distortion loss can be used as a regularization term, effectively maintaining pairwise distance relationships during embedding. We also show that Gaussian kernel embedding is a form of minimum-distortion embedding. Furthermore, we analyze and compare the strengths of different distortion measures through theoretical analysis. Finally, we demonstrate the effectiveness of distortion regularization across multiple downstream tasks using benchmark datasets. The results confirm that regularization based on distortion is effective and generally improves the performance of downstream tasks.

TL;DR: This paper introduces a method to control distortion during graph embedding.