MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis

TL;DR

MAPLE is a novel self-supervised nonlinear dimensionality reduction technique that improves manifold modeling and visualization of complex high-dimensional data.

Contribution

It enhances UMAP with self-supervised learning and MMCRs to better capture manifold geometry and improve cluster separation.

Findings

Produces clearer visual cluster separations than UMAP.

Resolves finer subclusters in high-dimensional data.

Maintains computational efficiency.

Abstract

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to this approach are maximum manifold capacity representations (MMCRs), which help untangle complex manifolds by compressing variances among locally similar data points while amplifying variance among dissimilar data points. This design is particularly effective for high-dimensional data with substantial intra-cluster variance and curved manifold structures, such as biological or image data. Our qualitative and quantitative evaluations demonstrate that MAPLE can produce clearer visual cluster separations and finer subcluster resolution than UMAP while maintaining tractable computational cost.