序数多维标度的理论基础，含内部展开与外部展开
统计理论
2025-06-19 v3 统计理论
摘要
我们提供了序数多维标度多个变体的综合理论，包括内部展开与外部展开。我们首先遵循 Shepard (1966) 并在连续统模型中工作以获得洞见。随后我们遵循 Kleindessner 与 von Luxburg (2014) 并在渐近离散设定下工作。
引用
@article{arxiv.2310.00211,
title = {Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding},
author = {Ery Arias-Castro and Clément Berenfeld and Daniel Kane},
journal= {arXiv preprint arXiv:2310.00211},
year = {2025}
}
备注
final version, focusing on the point model and with discrete-to-continuous convergence, to be published in SIMODS