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Nonlinear dimensionality reduction methods are a popular tool for datascientists and researchers to visualize complex, high dimensional data.However, while these methods continue to improve and grow in number, it isoften difficult to evaluate the quality of a visualization due to a variety offactors such as lack of information about the intrinsic dimension of the dataand additional tuning required for many evaluation metrics. In this paper, weseek to provide a systematic comparison of dimensionality reduction qualitymetrics using datasets where we know the ground truth manifold. We utilize eachmetric for hyperparameter optimization in popular dimensionality reductionmethods used for visualization and provide quantitative metrics to objectivelycompare visualizations to their original manifold. In our results, we find afew methods that appear to consistently do well and propose the best performeras a benchmark for evaluating dimensionality reduction based visualizations.

Spectral Overlap and a Comparison of Parameter-Free, Dimensionality Reduction Quality Metrics