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

TL;DR

MAPLE tackles the misalignment between high-dimensional neighborhood structure and low-dimensional visualizations by introducing a geometry-aware, self-supervised learning stage that refines the neighborhood graph via maximum manifold capacity representations (MMCR). It encodes data in a learned embedding with an encoder–projector pair and optimizes a MMCR loss that compresses variance within local neighborhoods while diversifying centroid directions, then applies a refined fuzzy-graph layout in the UMAP framework. Across image and single-cell datasets, MAPLE achieves clearer cluster separations and finer intra-cluster substructure with runtime comparable to other parametric DR methods, illustrating the practical impact of geometry-aware SSL in visual analytics. This work suggests that geometry-aware SSL can be broadly integrated into graph-based DR pipelines to improve manifold modeling and downstream interpretability, including multimodal data contexts.

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 comparable computational cost.

Figures (7)

• Figure 1: Conceptual overview of MAPLE. Self-supervised neighborhood refinement turns a cross-connected, entangled $k$NN graph into a simplified geometry that supports clearer graph layouts.
• Figure 2: The MAPLE pipeline, consisting of two phases: (1) graph construction and (2) graph layout. Phase 1 learns a graph representation of the input data through three steps that integrate SSL with MMCRs. Phase 2 performs the cross-entropy-based layout optimization, following UMAP. MAPLE's core contribution lies in Phase 1.
• Figure 3: Layouts of image (MNIST deng2012mnist, Fashion-MNIST xiao2017fashion, STL-10 coates2011analysis) and single-cell datasets (C. elegans subsets packer2019lineage and PBMC 4K) using MAPLE and baseline methods. MAPLE preserves both global structure and local neighborhoods more consistently across datasets.
• Figure 4: Closer visual inspection of MAPLE layouts on the Fashion-MNIST dataset (same layout as in \ref{['fig:comp']}). (a) Underlying average images of the trouser class. (b) Underlying average images from the coat/dress region.
• Figure 5: Completion time of MAPLE and UMAP in seconds. Left: runtime with varying feature dimensions ($D$) at fixed $N=10,000$. Right: runtime with varying data sizes ($N$) at fixed $D=784$. Solid and dotted lines indicate neighborhood sizes of $k=15$ and $k=30$, respectively. Both axes are shown on logarithmic scales, with tick labels $10^2$ and $10^3$ indicate orders of magnitude.