TopoMap++: A faster and more space efficient technique to compute projections with topological guarantees

Autor:	Guardieiro, Vitoria, de Oliveira, Felipe Inagaki, Doraiswamy, Harish, Nonato, Luis Gustavo, Silva, Claudio
Rok vydání:	2024
Předmět:	Computer Science - Graphics Computer Science - Computational Geometry Computer Science - Computer Vision and Pattern Recognition Computer Science - Human-Computer Interaction Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: This is the author's version of the article that has been accepted for publication in IEEE Transactions on Visualization and Computer Graphics (TVCG)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.07257 Zobrazit plný text záznamu View this record from Arxiv