The Rashomon Effect for Visualizing High-Dimensional Data

2026-04-01

AI Summary

This work addresses the non-uniqueness inherent in dimensionality reduction of high-dimensional data, where a single embedding often fails to simultaneously preserve local structure, ensure interpretability, and align with external knowledge. To overcome this limitation, the paper proposes modeling the Rashomon set of dimensionality reduction—i.e., the collection of multiple equally valid, high-quality embeddings—and extracting stable adjacency relationships from this set to enhance embedding robustness. Methodologically, it introduces PCA-guided alignment to improve axis interpretability, incorporates concept-alignment regularization to integrate external semantic knowledge, and jointly optimizes the embedding geometry. The resulting visualizations maintain strong local and global structural fidelity while significantly improving interpretability and alignment with user-defined objectives.

Abstract

Dimension reduction (DR) is inherently non-unique: multiple embeddings can preserve the structure of high-dimensional data equally well while differing in layout or geometry. In this paper, we formally define the Rashomon set for DR -- the collection of `good' embedding -- and show how embracing this multiplicity leads to more powerful and trustworthy representations. Specifically, we pursue three goals. First, we introduce PCA-informed alignment to steer embeddings toward principal components, making axes interpretable without distorting local neighborhoods. Second, we design concept-alignment regularization that aligns an embedding dimension with external knowledge, such as class labels or user-defined concepts. Third, we propose a method to extract common knowledge across the Rashomon set by identifying trustworthy and persistent nearest-neighbor relationships, which we use to construct refined embeddings with improved local structure while preserving global relationships. By moving beyond a single embedding and leveraging the Rashomon set, we provide a flexible framework for building interpretable, robust, and goal-aligned visualizations.

Problem

• dimension reduction
• Rashomon effect
• embedding non-uniqueness
• visualization interpretability
• high-dimensional data

Innovation

• Rashomon set
• dimension reduction
• PCA-informed alignment
• concept-alignment regularization
• trustworthy nearest neighbors