Does Dimensionality Reduction via Random Projections Preserve Landscape Features?

2026-04-14

AI Summary

This study addresses the challenge of preserving landscape characteristics in exploratory landscape analysis (ELA) under dimensionality reduction for high-dimensional black-box optimization. Due to data sparsity and high computational costs, ELA is often applied in reduced-dimensional spaces, yet it remains unclear whether such projections retain the essential properties of the original problem landscapes. The paper presents the first systematic evaluation of how random Gaussian embeddings (RGE) affect the fidelity of ELA features, employing multi-scale sampling to compute and compare features across varying embedding dimensions. The findings reveal that most ELA features are highly sensitive to random projections, with linear dimensionality reduction typically distorting their geometric and topological structures. Moreover, even seemingly stable features may arise from projection artifacts rather than intrinsic problem properties, thereby challenging the common assumption that reduced-space features reliably represent the original optimization landscape.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Exploratory Landscape Analysis
• Dimensionality Reduction
• Random Projections
• Black-box Optimization
• Landscape Features

Innovation

• Exploratory Landscape Analysis
• Random Projections
• Dimensionality Reduction
• Black-box Optimization
• Landscape Robustness