# Local Intrinsic Dimensionality Measures for Graphs, with Applications to Graph Embeddings

arXiv: https://arxiv.org/abs/2208.11986 · HTML: https://mlsanity.com/paper/2208.11986/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Subspace Determination through Local Intrinsic Dimensional Decomposition: Theory and Experimentation](https://mlsanity.com/paper/1907.06771/) (2019)

## Built on by (most cited first, 3 of 3)

- [Local Intrinsic Dimensionality for Dynamic Graph Embeddings](https://mlsanity.com/paper/2411.16145/) (2024)
- [On the Use of Bagging for Local Intrinsic Dimensionality Estimation](https://mlsanity.com/paper/2603.24384/) (2026)
- [Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding](https://mlsanity.com/paper/2608.18762/) (2026)

## Abstract (arXiv)

The notion of local intrinsic dimensionality (LID) is an important advancement in data dimensionality analysis, with applications in data mining, machine learning and similarity search problems. Existing distance-based LID estimators were designed for tabular datasets encompassing data points represented as vectors in a Euclidean space. After discussing their limitations for graph-structured data considering graph embeddings and graph distances, we propose NC-LID, a novel LID-related measure for quantifying the discriminatory power of the shortest-path distance with respect to natural communities of nodes as their intrinsic localities. It is shown how this measure can be used to design LID-aware graph embedding algorithms by formulating two LID-elastic variants of node2vec with personalized hyperparameters that are adjusted according to NC-LID values. Our empirical analysis of NC-LID on a large number of real-world graphs shows that this measure is able to point to nodes with high link reconstruction errors in node2vec embeddings better than node centrality metrics. The experimental evaluation also shows that the proposed LID-elastic node2vec extensions improve node2vec by better preserving graph structure in generated embeddings.