How Scale Breaks "Normalized Stress" and KL Divergence: Rethinking Quality Metrics

Area of Science:

• Data visualization
• Machine learning
• Computational biology
• Social sciences

Background:

• High-dimensional data visualization relies on 2D scatter plots.
• Quality metrics like normalized stress and Kullback-Leibler (KL) divergence assess projection accuracy.
• Current metrics are sensitive to uniform scaling, impacting evaluation reliability.

Purpose of the Study:

• To investigate the impact of uniform scaling on normalized stress and KL divergence.
• To develop a scale-invariant method for improving these dimension reduction quality metrics.
• To validate the proposed technique using analytical and empirical methods.

Main Methods:

• Analytical investigation of scaling effects on stress and KL divergence.
• Empirical evaluation of metric behavior under uniform scaling.
• Development and application of a novel scale-invariant adjustment technique.

Main Results:

• Demonstrated significant sensitivity of normalized stress and KL divergence to uniform scaling.
• Quantified the extent to which scaling affects metric values and dimension reduction evaluations.
• Showcased the effectiveness of the proposed scale-invariant technique on a benchmark dataset.

Conclusions:

• Uniform scaling poses a challenge for accurate interpretation of dimension reduction quality metrics.
• The introduced scale-invariant technique offers a reliable solution for evaluating projection faithfulness.
• This advancement improves the assessment of complex, high-dimensional data visualization techniques.