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

arXiv: https://arxiv.org/abs/2308.16403 · HTML: https://mlsanity.com/paper/2308.16403/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Why Random Reshuffling Beats Stochastic Gradient Descent](https://mlsanity.com/paper/1510.08560/) (2015)
- [Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and Survey](https://mlsanity.com/paper/2109.02508/) (2021)
- [A Sparse Stress Model](https://mlsanity.com/paper/1608.08909/) (2016)
- [DRGraph: An Efficient Graph Layout Algorithm for Large-scale Graphs by Dimensionality Reduction](https://mlsanity.com/paper/2008.07799/) (2020)
- [Stochastic Gradient Descent Works Really Well for Stress Minimization](https://mlsanity.com/paper/2008.10376/) (2020)
- [Browser-based Hyperbolic Visualization of Graphs](https://mlsanity.com/paper/2205.08028/) (2022)
- [Spherical Graph Drawing by Multi-dimensional Scaling](https://mlsanity.com/paper/2209.00191/) (2022)

## Built on by (most cited first, 5 of 5)

- [DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction](https://mlsanity.com/paper/2508.13747/) (2025)
- [Node Embeddings via Neighbor Embeddings](https://mlsanity.com/paper/2503.23822/) (2025)
- [DyGSSM: Multi-view Dynamic Graph Embeddings with State Space Model Gradient Update](https://mlsanity.com/paper/2505.09017/) (2025)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [Class Angular Distortion Index for Dimensionality Reduction](https://mlsanity.com/paper/2605.00637/) (2026)

## Abstract (arXiv)

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.