Visualizing Uncertainty in Non-linear Projections with Ensembles

2026-08-14

AI Summary

This study addresses the challenges of projection instability and noise overfitting in nonlinear dimensionality reduction, which hinder reliable structural assessment. We propose a consensus embedding framework based on ensemble medians and data perturbation. By integrating median-based visualization with input perturbation strategies, this approach effectively synthesizes the strengths of algorithms such as UMAP and t-SNE. The method preserves standard quality metrics while significantly enhancing global structure representation, thereby achieving an optimal balance between global and local topologies. Furthermore, it precisely reveals the reliability of projection patterns, establishing a novel paradigm for evaluating the trustworthiness of nonlinear dimensionality reduction results.

Abstract

Widely used non-linear dimensionality reduction (NLDR) methods such as UMAP and t-SNE are stochastic--repeated runs on the same data can produce different low-dimensional projections. In this paper, we explore two problems related to projection variability: on some datasets clusters, structure, and outliers may change run-to-run, and on others projections can be extremely stable when overfitting noise. To address the first problem, we propose visualizing the median of multiple NLDR outputs rather than relying on individual projections. To address the second, we perturb input data before creating consensus embeddings. We find that taking the median of multiple projections performs comparably to individual runs on multiple quality metrics, while increasing perturbation emphasizes global over local structure. We show through a set of exploratory visualizations that even relatively simple ensemble presentations can be used to better communicate the reliability of projection patterns.

Problem

• Non-linear Dimensionality Reduction
• Projection Variability
• Uncertainty Visualization
• Stochastic Embeddings

Innovation

• Uncertainty Visualization
• Ensemble Embeddings
• Non-linear Dimensionality Reduction
• Data Perturbation
• Median Projection