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.

翻译：探索性景观分析（ELA）为刻画黑箱优化问题提供数值特征。然而在高维场景下，ELA面临稀疏效应、估计量方差大以及计算若干特征类别的极高成本等问题。因此，降维被提出作为使ELA适用于此类场景的手段，但尚不明确的是，在降维空间中计算的特征是否仍能反映原始景观的内在属性。本研究通过随机高斯嵌入（RGE）考察ELA特征在降维下的鲁棒性。我们从相同的采样点和目标值出发，在投影空间中计算ELA特征，并在多个样本预算和嵌入维度下将其与原始搜索空间中获得的特征进行比较。结果表明，线性随机投影常会改变与ELA相关的几何和拓扑结构，导致特征值不再代表原始问题。虽然少数特征保持相对稳定，但多数特征对嵌入高度敏感。此外，投影下的鲁棒性未必意味着信息性，因为看似鲁棒的特征仍可能反映投影引入的伪影，而非内在的景观特征。