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.
| Comments: | The paper is accepted in AISTATS 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.00485 [cs.LG] |
| (or arXiv:2604.00485v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.00485 arXiv-issued DOI via DataCite |
From: Yiyang Sun [view email]
[v1]
Wed, 1 Apr 2026 05:02:04 UTC (38,650 KB)
[v2]
Mon, 27 Apr 2026 19:38:03 UTC (38,646 KB)
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