Does Dimensionality Reduction via Random Projections Preserve Landscape Features?

arXiv cs.LG / 4/16/2026

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Key Points

The paper studies whether Exploratory Landscape Analysis (ELA) features remain faithful to original high-dimensional black-box optimization landscapes after dimensionality reduction using random Gaussian embeddings.
Using identical sampled points and objective values, it computes ELA features in both the original and projected spaces across varying sample budgets and embedding dimensions to assess feature robustness.
It finds that random linear projections often change the geometric and topological structure that ELA relies on, making many projected feature values non-representative of the original problem.
Although a small subset of ELA features can appear comparatively stable, most features are highly sensitive to the embedding dimension and projection details.
The authors caution that projection-robustness does not guarantee true informativeness, since robust-looking features may still capture artifacts introduced by the dimensionality reduction.

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.