# Does Dimensionality Reduction via Random Projections Preserve Landscape Features?

arXiv: https://arxiv.org/abs/2604.13230 · HTML: https://mlsanity.com/paper/2604.13230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning](https://mlsanity.com/paper/1711.08921/) (2017)
- [Exploratory Landscape Analysis is Strongly Sensitive to the Sampling Strategy](https://mlsanity.com/paper/2006.11135/) (2020)
- [IOHexperimenter: Benchmarking Platform for Iterative Optimization Heuristics](https://mlsanity.com/paper/2111.04077/) (2021)
- [Per-run Algorithm Selection with Warm-starting using Trajectory-based Features](https://mlsanity.com/paper/2204.09483/) (2022)
- [Landscape-Aware Fixed-Budget Performance Regression and Algorithm Selection for Modular CMA-ES Variants](https://mlsanity.com/paper/2006.09855/) (2020)
- [Towards Explainable Exploratory Landscape Analysis: Extreme Feature Selection for Classifying BBOB Functions](https://mlsanity.com/paper/2102.00736/) (2021)
- [High Dimensional Bayesian Optimization with Kernel Principal Component Analysis](https://mlsanity.com/paper/2204.13753/) (2022)
- [Towards Exploratory Landscape Analysis for Large-scale Optimization: A Dimensionality Reduction Framework](https://mlsanity.com/paper/2104.10301/) (2021)

## Abstract (arXiv)

Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems. In high-dimensional settings, however, ELA suffers from sparsity effects, high estimator variance, and the prohibitive cost of computing several feature classes. Dimensionality reduction has therefore been proposed as a way to make ELA applicable in such settings, but it remains unclear whether features computed in reduced spaces still reflect intrinsic properties of the original landscape. In this work, we investigate the robustness of ELA features under dimensionality reduction via Random Gaussian Embeddings (RGEs). Starting from the same sampled points and objective values, we compute ELA features in projected spaces and compare them to those obtained in the original search space across multiple sample budgets and embedding dimensions. Our results show that linear random projections often alter the geometric and topological structure relevant to ELA, yielding feature values that are no longer representative of the original problem. While a small subset of features remains comparatively stable, most are highly sensitive to the embedding. Moreover, robustness under projection does not necessarily imply informativeness, as apparently robust features may still reflect projection-induced artifacts rather than intrinsic landscape characteristics.