This study investigates privacy leakage in dimensionality reduction methods through a novel machine learning-based reconstruction attack. Employing an \emph{informed adversary} threat model, we develop a neural network capable of reconstructing high-dimensional data from low-dimensional embeddings. We evaluate six popular dimensionality reduction techniques: PCA, sparse random projection (SRP), multidimensional scaling (MDS), Isomap, $t$-SNE, and UMAP. Using both MNIST and NIH Chest X-ray datasets, we perform a qualitative analysis to identify key factors affecting reconstruction quality. Furthermore, we assess the effectiveness of an additive noise mechanism in mitigating these reconstruction attacks.

翻译：本研究通过一种新颖的基于机器学习的重构攻击方法，探究降维技术中的隐私泄露问题。采用"知情对手"威胁模型，我们构建了一种能够从低维嵌入中重构高维数据的神经网络。我们评估了六种主流降维技术：主成分分析（PCA）、稀疏随机投影（SRP）、多维标度法（MDS）、等距特征映射（Isomap）、$t$-分布随机邻域嵌入（$t$-SNE）以及均匀流形逼近与投影（UMAP）。基于MNIST手写数字数据集和美国国立卫生研究院胸部X射线数据集，我们通过定性分析揭示了影响重构质量的关键因素。此外，我们评估了加性噪声机制在缓解此类重构攻击方面的有效性。