FloDR Offers Invertible Dimensionality Reduction with Diagnostic Visualizations.

Traditional dimensionality reduction techniques like t-SNE and UMAP often discard crucial information during the optimization process, leading to misinterpretations of distances, cluster meanings, and empty spaces in their two-dimensional embeddings. This new research presents FloDR (Flow-based Dimensionality Reduction), an innovative method that addresses these limitations by embedding data through an invertible normalizing flow. While FloDR still produces a 2D embedding, it crucially retains the remaining high-dimensional coordinates rather than discarding them. A key advantage of FloDR is its ability to provide an exact inverse and an exact density for the trained mapping. These properties enable the creation of powerful diagnostic visualizations that are computed directly from the model's inverse, offering a more accurate understanding of the embedding. Specifically, FloDR generates two fields: the "conditional spread," which quantifies how much of the original data remains undetermined at each embedding position, and the "hidden contrast," which measures the information about a labeled contrast that the plotted 2D coordinates discard. Both diagnostic fields are rendered with a prespecified statistical test against held-out data and bootstrap confidence, indicating when a field's interpretation is unreliable. By making the information loss explicit and providing tools to interpret the embedding's true meaning, FloDR significantly enhances the reliability and depth of insights derived from dimensionality reduction, moving beyond superficial visual patterns.