随机投影会扭曲优化问题的结构,导致特征失真。
Does Dimensionality Reduction via Random Projections Preserve Landscape Features?

- 用随机高斯嵌入降低维度,对比原空间特征变化。
- 多数特征值在降维后明显偏移,无法反映原始问题特性。
- 部分特征看似稳定,实则可能反映投影伪影而非真实结构。
探索性景观分析(ELA)通过数值特征刻画黑箱优化问题。但在高维场景下,ELA面临稀疏效应、估计方差大及计算成本高的问题。因此有人提出用降维使ELA适用于高维场景,但尚不清楚降维后的特征是否仍能反映原始景观的本质属性。本文研究了通过随机高斯嵌入(RGEs)进行降维对ELA特征的影响。基于相同的采样点和目标值,在不同采样预算与嵌入维度下,比较投影空间与原始搜索空间中的ELA特征。结果表明,线性随机投影常改变与ELA相关的几何与拓扑结构,导致特征值不再代表原问题。虽然少数特征相对稳定,但大多数特征对嵌入高度敏感。此外,投影下的鲁棒性并不等同于信息量,因为看似稳定的特征可能仅反映投影引入的伪影,而非内在景观特性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。