TopoMap++加速并压缩了高维数据可视化，保留拓扑结构。
TopoMap++: A faster and more space efficient technique to compute projections with topological guarantees
- 采用更紧凑布局和树形结构提升空间效率
- 算法速度显著提升，适合大规模数据
- 利用拓扑层级结构辅助交互探索
高维数据因特征多难以有效可视化。降维技术如PCA、UMAP和t-SNE通过将数据投影到低维空间来保留关键关系。TopoMap能更好保持数据底层结构，生成可解释的可视化结果，其核心是保证高维数据与可视化空间的Rips过滤0维持久图一致。然而原始方法计算慢且布局稀疏，难以处理复杂大数据。本文提出三项改进：1）更节省空间的布局；2）显著更快的实现；3）基于树形图（TreeMap）的新表示法，利用拓扑层次结构支持可视化探索。这些改进使新版本称为TopoMap++，在多个应用场景中展示了更强的可视化能力。
原文摘要 · Abstract (English)
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional space while preserving important relationships. TopoMap is another technique that excels at preserving the underlying structure of the data, leading to interpretable visualizations. In particular, TopoMap maps the high-dimensional data into a visual space, guaranteeing that the 0-dimensional persistence diagram of the Rips filtration of the visual space matches the one from the high-dimensional data. However, the original TopoMap algorithm can be slow and its layout can be too sparse for large and complex datasets. In this paper, we propose three improvements to TopoMap: 1) a more space-efficient layout, 2) a significantly faster implementation, and 3) a novel TreeMap-based representation that makes use of the topological hierarchy to aid the exploration of the projections. These advancements make TopoMap, now referred to as TopoMap++, a more powerful tool for visualizing high-dimensional data which we demonstrate through different use case scenarios.
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