Curvature Regularization to Prevent Distortion in Graph Embedding
This work tackles the problem of distorted graph topology patterns in Euclidean embedding space, which makes detection difficult for machine learning models, and offers an incremental improvement to existing graph embedding methods.
This paper addresses the problem of distortion in graph topology patterns when embedded into Euclidean space, even if proximity is preserved within the manifold. The authors propose curvature regularization, using a novel angle-based sectional curvature (ABS curvature), to enforce flatness in embedding manifolds and prevent this distortion. Integrating this regularization into five existing embedding methods resulted in significant improvements across various open graph datasets in two applications.
Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this proximity-preserving strategy: Graph topology patterns, while preserved well into an embedding manifold by preserving proximity, may distort in the ambient embedding Euclidean space, and hence to detect them becomes difficult for machine learning models. To address the problem, we propose curvature regularization, to enforce flatness for embedding manifolds, thereby preventing the distortion. We present a novel angle-based sectional curvature, termed ABS curvature, and accordingly three kinds of curvature regularization to induce flat embedding manifolds during graph embedding. We integrate curvature regularization into five popular proximity-preserving embedding methods, and empirical results in two applications show significant improvements on a wide range of open graph datasets.