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This paper formalizes the concept of a "Rashomon set" for dimension reduction (DR), representing the collection of equally valid embeddings, and leverages this set to improve visualization trustworthiness and interpretability. They introduce PCA-informed alignment to orient embeddings along principal components and concept-alignment regularization to align dimensions with external knowledge. Finally, they extract common knowledge across the Rashomon set to refine embeddings, improving local structure while preserving global relationships.
Instead of seeking a single "best" dimension reduction, embrace the multiplicity of good embeddings to build more robust and interpretable visualizations.
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.