# Multi-Objective Genetic Programming for Manifold Learning: Balancing Quality and Dimensionality

arXiv: https://arxiv.org/abs/2001.01331 · HTML: https://mlsanity.com/paper/2001.01331/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2020.

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

- [On genetic programming representations and fitness functions for interpretable dimensionality reduction](https://mlsanity.com/paper/2203.00528/) (2022)
- [Genetic Programming for Manifold Learning: Preserving Local Topology](https://mlsanity.com/paper/2108.09914/) (2021)
- [Mining Feature Relationships in Data](https://mlsanity.com/paper/2102.01355/) (2021)
- [Evolutionary Computation for the Design and Enrichment of General-Purpose Artificial Intelligence Systems: Survey and Prospects](https://mlsanity.com/paper/2407.08745/) (2024)
- [Genetic Programming for Explainable Manifold Learning](https://mlsanity.com/paper/2403.14139/) (2024)

## Abstract (arXiv)

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially reduce the dimensionality of a dataset while preserving as much information as possible. However, state-of-the-art manifold learning algorithms are opaque in how they perform this transformation. Understanding the way in which the embedding relates to the original high-dimensional space is critical in exploratory data analysis. We previously proposed a Genetic Programming method that performed manifold learning by evolving mappings that are transparent and interpretable. This method required the dimensionality of the embedding to be known a priori, which makes it hard to use when little is known about a dataset. In this paper, we substantially extend our previous work, by introducing a multi-objective approach that automatically balances the competing objectives of manifold quality and dimensionality. Our proposed approach is competitive with a range of baseline and state-of-the-art manifold learning methods, while also providing a range (front) of solutions that give different trade-offs between quality and dimensionality. Furthermore, the learned models are shown to often be simple and efficient, utilising only a small number of features in an interpretable manner.