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

TL;DR

The paper introduces the Gap Index, a new metric for evaluating 2D dimensionality reduction projections by measuring distortion in empty regions through triangular decomposition. It detects visually significant structural changes that traditional metrics miss, offering both a global score and localized distortion visualization. The method is efficient and interpretable, enhancing trust in visual data analysis.

Why It Matters

Visual analysis of high-dimensional data relies heavily on projections, but existing quality metrics often overlook distortions in empty spaces, which can mislead interpretation. The Gap Index improves reliability by identifying subtle yet impactful layout changes, supporting more accurate data exploration and decision-making.

Key Findings

• The Gap Index detects visual distortions in empty regions of 2D projections that are missed by conventional metrics focused on point distances or neighborhoods.
• It uses triangulation of empty space to compute deformation per triangle, enabling both a global scalar score and spatially resolved distortion maps.
• The metric is computationally efficient, sensitive to small but visually meaningful changes, and provides interpretable feedback for users.