"Normalized Stress" is Not Normalized: How to Interpret Stress Correctly
This addresses a problem for researchers in machine learning and data visualization who rely on accurate metrics to assess dimension reduction methods, though it is incremental as it modifies an existing metric.
The paper tackles the issue that normalized stress, a widely used quality metric for dimension reduction projections, is not scale-invariant, which can mislead evaluations of projection techniques. The authors introduce a simple method to make normalized stress scale-invariant and demonstrate its effectiveness on a benchmark.
Stress is among the most commonly employed quality metrics and optimization criteria for dimension reduction projections of high dimensional data. Complex, high dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two dimensional scatter plots that visually capture some properties of the data. Because visually determining the accuracy of these plots is challenging, researchers often use quality metrics to measure projection accuracy or faithfulness to the full data. One of the most commonly employed metrics, normalized stress, is sensitive to uniform scaling of the projection, despite this act not meaningfully changing anything about the projection. We investigate the effect of scaling on stress and other distance based quality metrics analytically and empirically by showing just how much the values change and how this affects dimension reduction technique evaluations. We introduce a simple technique to make normalized stress scale invariant and show that it accurately captures expected behavior on a small benchmark.