# On genetic programming representations and fitness functions for interpretable dimensionality reduction

arXiv: https://arxiv.org/abs/2203.00528 · HTML: https://mlsanity.com/paper/2203.00528/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 1 Mar 2022.

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

- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Revisiting Small Batch Training for Deep Neural Networks](https://mlsanity.com/paper/1804.07612/) (2018)
- [A Weighted Correlation Index for Rankings with Ties](https://mlsanity.com/paper/1404.3325/) (2014)
- [Learning a Formula of Interpretability to Learn Interpretable Formulas](https://mlsanity.com/paper/2004.11170/) (2020)
- [On Explaining Machine Learning Models by Evolving Crucial and Compact Features](https://mlsanity.com/paper/1907.02260/) (2019)
- [Genetic Programming for Evolving a Front of Interpretable Models for Data Visualisation](https://mlsanity.com/paper/2001.09578/) (2020)
- [Differentiable Genetic Programming](https://mlsanity.com/paper/1611.04766/) (2016)
- [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)
- [Genetic Programming for Evolving Similarity Functions for Clustering: Representations and Analysis](https://mlsanity.com/paper/1910.10264/) (2019)

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

- [Evolutionary approaches to explainable machine learning](https://mlsanity.com/paper/2306.14786/) (2023)
- [Evolutionary Computation and Explainable AI: A Roadmap to Understandable Intelligent Systems](https://mlsanity.com/paper/2406.07811/) (2024)
- [Non-linear PCA via Evolution Strategies: a Novel Objective Function](https://mlsanity.com/paper/2602.03967/) (2026)

## Abstract (arXiv)

Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its lower-dimensional representation (e.g., MDS, t-SNE, isomap), or produce mappings that cannot be easily interpreted (e.g., kernel PCA, neural-based autoencoder). Recently, genetic programming (GP) has been used to evolve interpretable DR mappings in the form of symbolic expressions. There exists a number of ways in which GP can be used to this end and no study exists that performs a comparison. In this paper, we fill this gap by comparing existing GP methods as well as devising new ones. We evaluate our methods on several benchmark datasets based on predictive accuracy and on how well the original features can be reconstructed using the lower-dimensional representation only. Finally, we qualitatively assess the resulting expressions and their complexity. We find that various GP methods can be competitive with state-of-the-art DR algorithms and that they have the potential to produce interpretable DR mappings.