# Genetic Programming for Manifold Learning: Preserving Local Topology

arXiv: https://arxiv.org/abs/2108.09914 · HTML: https://mlsanity.com/paper/2108.09914/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 56 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [ANN-Benchmarks: A Benchmarking Tool for Approximate Nearest Neighbor Algorithms](https://mlsanity.com/paper/1807.05614/) (2018)
- [Genetic Programming for Evolving a Front of Interpretable Models for Data Visualisation](https://mlsanity.com/paper/2001.09578/) (2020)
- [Can Genetic Programming Do Manifold Learning Too?](https://mlsanity.com/paper/1902.02949/) (2019)
- [Multi-Objective Genetic Programming for Manifold Learning: Balancing Quality and Dimensionality](https://mlsanity.com/paper/2001.01331/) (2020)

## Built on by (most cited first, 2 of 2)

- [SlideBot: A Multi-Agent Framework for Generating Informative, Reliable, Multi-Modal Presentations](https://mlsanity.com/paper/2511.09804/) (2025)
- [Evolutionary Computation and Explainable AI: A Roadmap to Understandable Intelligent Systems](https://mlsanity.com/paper/2406.07811/) (2024)

## Abstract (arXiv)

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear transformations that preserve the most important structure of the original data. State-of-the-art manifold learning methods directly optimise an embedding without mapping between the original space and the discovered embedded space. This makes interpretability - a key requirement in exploratory data analysis - nearly impossible. Recently, genetic programming has emerged as a very promising approach to manifold learning by evolving functional mappings from the original space to an embedding. However, genetic programming-based manifold learning has struggled to match the performance of other approaches. In this work, we propose a new approach to using genetic programming for manifold learning, which preserves local topology. This is expected to significantly improve performance on tasks where local neighbourhood structure (topology) is paramount. We compare our proposed approach with various baseline manifold learning methods and find that it often outperforms other methods, including a clear improvement over previous genetic programming approaches. These results are particularly promising, given the potential interpretability and reusability of the evolved mappings.