Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold

TL;DR

This paper introduces WEIGHTED-PM, a novel method for embedding heterogeneous graphs into weighted product manifolds, which adaptively assigns importance to different geometric components to better capture complex graph structures.

Contribution

It proposes a data-driven approach to weight component spaces in product manifolds for improved graph embedding, addressing limitations of previous equal-role assumptions.

Findings

Outperforms existing methods on synthetic and real-world datasets.

Achieves lower geometric distortion in graph representations.

Enhances performance on downstream tasks like recommendation and knowledge graph embedding.

Abstract

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited capacity in representing graphs of varying structures. A promising candidate for the faithful embedding of data with varying structure is product manifolds of component spaces of different geometries (spherical, hyperbolic, or euclidean). In this paper, we take a closer look at the structure of product manifold embedding spaces and argue that each component space in a product contributes differently to expressing structures in the input graph, hence should be weighted accordingly. This is different from previous works which consider the roles of different components equally. We then propose WEIGHTED-PM, a data-driven method for learning embedding of heterogeneous graphs in weighted product manifolds. Our method utilizes the topological information of the input graph to automatically determine the weight of each component in product spaces. Extensive experiments on synthetic and real-world graph datasets demonstrate that WEIGHTED-PM is capable of learning better graph representations with lower geometric distortion from input data, and performs better on multiple downstream tasks, such as word similarity learning, top-$k$ recommendation, and knowledge graph embedding.