IEEE VIS 2024 Content: TopoMap++: A faster and more space efficient technique to compute projections with topological guarantees

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

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 Vitoria Guardieiro - New York University, New York City, United States

 Felipe Inagaki de Oliveira - New York University, New York City, United States

 Harish Doraiswamy - Microsoft Research India, Bangalore, India

 Luis Gustavo Nonato - University of Sao Paulo, Sao Carlos, Brazil

 Claudio Silva - New York University, New York City, United States

 Room: Bayshore V

2024-10-16T15:15:00Z GMT-0600 Change your timezone on the schedule page
2024-10-16T15:15:00Z

Exemplar figure, described by caption below — Representations of the MNIST database of handwritten digits. (a) This data is projected using TopoMap. (b) The hierarchy defined by the process of topological simplification is visualized as a TreeMap. Each leaf of this tree corresponds to the smallest simplified component with a user-defined minimum number of points. (c) The TopoMap++ representation of the same data where the eleven components selected by the TreeMap are highlighted. As can be seen, TopoMap++ makes much more efficient use of the space compared to TopoMap, thus allowing users to easily analyze the relationships between the different clusters.

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Keywords

Topological data analysis, Computational topology, High-dimensional data, Projection.

Abstract

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.