Despite its widespread use as a quality metric for dimensionality reduction techniques, normalized stress is sensitive to uniform scaling (stretching, shrinking) of the embedding. By exploring how normalized stress behaves on a variety of simple datasets, we can construct a safe and reliable variant, scale-normalized stress.
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This is a web application that contains an interactive figure. The interactive figure plots the "normalized" stress curves of MDS, t-SNE, and Random (points are randomly placed) embeddings over a range of scalars for various well-known datasets. The minimum value for each curve has been labeled with a point, the normalized stress score (y-coordinate) of which the authors denote as the scale-normalized stress score. By hovering over the point, the user can examine its exact x and y coordinates. The user also has the ability to select the dataset they would like to explore, toggle the dimensionality reduction (DR) techniques, observe how changing the scalar value for a given DR technique affects the ranking, and change the max value for the x-axis range (from 1 to 2000).
The code and instructions needed to reproduce the experiments upon which this graphical interface is based, including the implementation of scale-normalized stress, are made available on GitHub.
Published on July 7, 2024, and created by Kiran Smelser to demonstrate the issues with using normalized stress as a quality metric. Thanks to Professor Kobourov for pointing out that normalized stress is scale sensitive.
If you see a mistake or want to suggest a change, please create an issue on GitHub.