Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index

Authors

Jaume Ros (Eindhoven University of Technology), Alessio Arleo (Eindhoven University of Technology), Fernando V Paulovich (TU Eindhoven)

Presentation

Session

Great, now you scattered the data everywhere!

Time

Tuesday, Nov 10, 15:12 – 15:24 (US/Eastern) · session 15:00 – 16:30

Location

Hall Essex center

Keywords

Dimensionality reduction, quality metric

Abstract

Quality metrics play a crucial role in the proper use of dimensionality reduction projections for visual analysis of high-dimensional data. They quantify the degree of distortion of a projection compared to the high-dimensional data and provide a reliable indication of how confident users can be in the structures they see in the resulting layouts. However, most popular metrics focus on capturing direct relationships between points (e.g., distances or neighborhoods) while neglecting distortions in empty areas of the layout, even though these often compose visually relevant features of a 2D layout. In this paper, we introduce the Gap Index (GI), a quality metric for 2D projections that captures visual distortion by measuring spatial distortion in empty areas of a projection. It does so by decomposing the space into empty triangles, which are then compared to their high-dimensional counterparts to compute the deformation. This per-triangle deformation can be aggregated into a single scalar value or overlaid on a projection to visualize regional distortion patterns. Results show that, contrary to popular quality metrics, the GI is sensitive to small structural deformations that have high visual impact. It is also fast to compute and interpretable.

For Practitioners

Anyone who uses dimensionality reduction to visually analyze high-dimensional data. Particularly researchers from other domains that might not be as familiar with the possible distortions introduced in the projection.