提出QPAD方法，让高维向量降维后仍保持邻居关系准确
QPAD: Quantile-Preserving Approximate Dimension Reduction for Nearest Neighbors Preservation in High-Dimensional Vector Search
- 通过最大化近邻与非近邻的间距来保留邻居结构
- 在五个领域测试中优于11种主流降维方法
- 无需标注数据，可直接用于大规模向量检索
高维向量嵌入广泛应用于检索系统，但常受噪声、维度灾难和运行缓慢影响。然而，由于降维（DR）易破坏对搜索至关重要的最近邻（NN）结构，其应用仍较少。现有方法如PCA和UMAP优化全局或流形保持目标，而非检索特定目标。本文提出QPAD——一种无监督降维方法，通过在软正交约束下最大化k-NN与非k-NN之间的间隔，显式保留近似最近邻关系。我们分析了其复杂度与良好性质，该设计使QPAD能在不改变原始嵌入模型的前提下，保持近似最近邻相关几何结构，支持大规模向量检索并可索引用于近似最近邻（ANN）搜索。在五个领域的实验表明，QPAD在保留邻域结构方面持续优于11种标准降维方法，显著提升降维后的检索准确性。
原文摘要 · Abstract (English)
High-dimensional vector embeddings are widely used in retrieval systems, but they often suffer from noise, the curse of dimensionality, and slow runtime. However, dimensionality reduction (DR) is rarely applied due to its tendency to distort the nearest-neighbor (NN) structure that is critical for search. Existing DR techniques such as PCA and UMAP optimize global or manifold-preserving criteria, rather than retrieval-specific objectives. We present QPAD -- Quantile-Preserving Approximate Dimension Reduction, an unsupervised DR method that explicitly preserves approximate NN relations by maximizing the margin between k-NNs and non-k-NNs under a soft orthogonality constraint. We analyze its complexity and favorable properties. This design enables QPAD to retain ANN-relevant geometry without supervision or changes to the original embedding model, while supporting scalability for large-scale vector search and being indexable for ANN search. Experiments across five domains show that QPAD consistently outperforms eleven standard DR methods in preserving neighborhood structure, enabling more accurate search in reduced dimensions.
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