Balancing between the Local and Global Structures (LGS) in Graph Embedding

TL;DR

This paper introduces a tunable graph embedding method called LGS that balances local and global structural information, improving visualization quality by capturing intermediate structures effectively.

Contribution

The paper proposes a novel LGS method with a tunable parameter to balance local and global structures in graph embedding, along with a new quality metric for intermediate structure preservation.

Findings

LGS performs competitively with state-of-the-art methods on synthetic and real datasets.

LGS effectively balances local and global structure preservation in graph embeddings.

A new metric, cluster distance preservation, assesses intermediate structure capture.

Abstract

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.