系统梳理典型分析方法，揭示其在高维数据中的可解释建模优势。
A Survey on Archetypal Analysis
- 基于凸组合提取数据中的典型特征，实现可解释的降维与表征
- 涵盖跨学科应用案例，总结建模最佳实践与现有局限
- 适合关注可解释性建模与数据结构挖掘的研究者参考
典型分析（AA）由Adele Cutler和Leo Breiman于1994年提出，是一种从观测数据中提取代表性原型（即典型）的计算方法，每个观测可表示为这些典型成分的凸组合。该方法能提供直观、可解释且可追溯的特征提取与降维表示，有助于理解高维数据的内在结构，并广泛应用于多个科学领域。然而，其优化问题具有非凸性，带来挑战。本文是首篇全面综述，系统介绍AA的方法体系、跨学科应用、建模最佳实践及其局限性，并指出关键未来研究方向。
原文摘要 · Abstract (English)
Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure for extracting distinct aspects, so-called archetypes, from observations, with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data and enabling wide applications across the sciences. However, AA also faces challenges, particularly as the associated optimization problem is non-convex. This is the first survey that provides researchers and data mining practitioners with an overview of the methodologies and opportunities that AA offers, surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data with AA and its limitations. The survey concludes by explaining crucial future research directions concerning AA.
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