通过多重降维解构建可信可视化，提升可解释性与鲁棒性。
The Rashomon Effect for Visualizing High-Dimensional Data
- 定义降维的Rashomon集，包容多种有效嵌入方案。
- 利用主成分导向对齐，使坐标轴可解释且不破坏局部结构。
- 提取共性邻近关系，构建更稳定的局部结构可视化。
降维本质上是不唯一的：多个嵌入方案可在保持高维数据结构的同时，呈现不同的布局或几何形态。本文首次形式化定义了降维中的Rashomon集——即所有‘良好’嵌入的集合，并证明拥抱这种多样性能带来更强大、更可信的表示。具体而言，我们实现三个目标：首先，提出基于PCA的对齐方法，引导嵌入趋向主成分，使坐标轴可解释且不扭曲局部邻域；其次，设计概念对齐正则化，将嵌入维度与外部知识（如类别标签或用户定义概念）对齐；第三，提出从Rashomon集中提取共性知识的方法，识别稳定可靠的最近邻关系，据此构建优化局部结构但保留全局关系的精炼嵌入。通过超越单一嵌入，利用整个Rashomon集，我们提供了一个灵活、可解释、鲁棒且目标对齐的可视化框架。
原文摘要 · Abstract (English)
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.
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