TopoMap++: A Faster and More Space Efficient Technique to Compute Projections with Topological Guarantees

Area of Science:

• Data Visualization
• Computational Topology
• Machine Learning

Background:

• High-dimensional data visualization is challenging.
• Existing dimensionality reduction techniques like PCA, UMAP, and t-SNE project data to lower dimensions.
• TopoMap preserves data structure but can be slow and sparse for large datasets.

Purpose of the Study:

• To improve the TopoMap algorithm for better high-dimensional data visualization.
• To address limitations of speed and sparsity in the original TopoMap.
• To introduce a more powerful and interpretable visualization tool.

Main Methods:

• Developed a more space-efficient layout for TopoMap.
• Created a significantly faster implementation of the algorithm.
• Introduced a novel TreeMap-based representation utilizing topological hierarchy.

Main Results:

• The enhanced TopoMap, now TopoMap++, offers improved visualization capabilities.
• Demonstrated effectiveness through various use case scenarios.
• The new implementation is faster and produces denser, more interpretable layouts.

Conclusions:

• TopoMap++ provides a more powerful and efficient tool for visualizing high-dimensional data.
• The improvements make topological data analysis more accessible for complex datasets.
• The TreeMap representation aids in exploring projected data structures.