Progressive Uniform Manifold Approximation and Projection

Abstract

We present a progressive algorithm for the Uniform Manifold Approximation and Projection (UMAP), called the Progressive UMAP. Based on the theory of Riemannian geometry and algebraic topology, UMAP is an emerging dimensionality reduction technique that offers better versatility and stability than t-SNE. Although UMAP is also more efficient than t-SNE, it still suffers from an initial delay of a few minutes to produce the first projection, which limits its use in interactive data exploration. To tackle this problem, we improve the sequential computations in UMAP by making them progressive, which allows people to incrementally append a batch of data points into the projection at the desired pace. In our experiment with the Fashion MNIST dataset, we found that Progressive UMAP could generate the first approximate projection within a few seconds while also sufficiently capturing the important structures of the high-dimensional dataset.