The Rashomon Effect for Visualizing High-Dimensional Data

TL;DR

This paper explores the multiplicity of high-quality embeddings in dimension reduction, introducing methods to align, regularize, and extract trustworthy structures from the Rashomon set for more interpretable and robust visualizations.

Contribution

It formally defines the Rashomon set for DR and proposes techniques for alignment, concept regularization, and knowledge extraction to improve visualization trustworthiness.

Findings

PCA-informed alignment enhances interpretability without losing local structure.

Concept-alignment regularization incorporates external knowledge into embeddings.

Identifying persistent relationships yields refined, more reliable visualizations.

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.