DiRe通过图布局优化，保留数据全局结构与拓扑特征。
Dimensionality reduction for homological stability and global structure preservation
- 结合初始嵌入与图布局优化，提升降维效果
- 在基准测试中优于UMAP和tSNE的全局结构保持能力
- 适合需量化大尺度几何特性的研究场景
我们提出DiRe，一种基于力导向的降维框架，旨在保留全局结构和同调特征，同时在现代硬件上具备实用性。该方法结合初始嵌入与基于图的布局优化，并通过局部失真、上下文保留以及持久同调度量评估低维表示。在所考虑的基准套件中，DiRe提供了与UMAP和tSNE互补的权衡：它不单纯作为局部可视化启发式，而是为可利用贝蒂曲线和持久性图谱量化大规模几何特性的嵌入提供框架。
原文摘要 · Abstract (English)
We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware. The method combines an initial embedding with a graph-based layout optimization and evaluates the resulting low-dimensional representation using local distortion, context preservation, and persistent homology measures. Across the benchmark suite considered here, DiRe provides a complementary tradeoff to UMAP and tSNE: it is designed less as a purely local visualization heuristic and more as a framework for embeddings whose large-scale geometry can be quantified through Betti curves and persistence diagrams.
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