Does Dimensionality Reduction via Random Projections Preserve Landscape Features?

TL;DR

This study evaluates whether dimensionality reduction via random projections preserves the landscape features used in Exploratory Landscape Analysis for optimization problems.

Contribution

It provides an empirical assessment of the robustness of ELA features under random Gaussian embeddings in high-dimensional spaces.

Findings

Most ELA features are sensitive to random projections.

A small subset of features remains stable after projection.

Robust features may still reflect artifacts, not true landscape properties.

Abstract

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.