Spectral Overlap and a Comparison of Parameter-Free, Dimensionality Reduction Quality Metrics
This work addresses the challenge for data scientists and researchers in objectively comparing and optimizing visualizations from dimensionality reduction methods, though it is incremental as it compares existing metrics rather than introducing new ones.
The paper tackled the problem of evaluating the quality of nonlinear dimensionality reduction visualizations by systematically comparing parameter-free quality metrics on datasets with known ground truth manifolds, finding a few methods that consistently perform well and proposing the best performer as a benchmark.
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to evaluate the quality of a visualization due to a variety of factors such as lack of information about the intrinsic dimension of the data and additional tuning required for many evaluation metrics. In this paper, we seek to provide a systematic comparison of dimensionality reduction quality metrics using datasets where we know the ground truth manifold. We utilize each metric for hyperparameter optimization in popular dimensionality reduction methods used for visualization and provide quantitative metrics to objectively compare visualizations to their original manifold. In our results, we find a few methods that appear to consistently do well and propose the best performer as a benchmark for evaluating dimensionality reduction based visualizations.