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Abstract <p>This work establishes a formulation of the classical multidimensional scaling in which the pairwise distances are corrupted by independent additive Gaussian noise. This formulation yields a stress objective function, derived from an explicit probabilistic model, allowing for a rigorous statistical analysis. Up to rotations and translations, we also prove the consistency of the estimator when the noise vanishes and prove finite-sample probability bounds on the estimation error. Our results complement the recently developed theories by focusing on a fixed size of data with increasingly accurate distance measurements.</p>

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On the Consistency of Multidimensional Scaling under Gaussian Noise: A Maximum Likelihood Framework

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Chanon Thongprayoon

摘要

Abstract

This work establishes a formulation of the classical multidimensional scaling in which the pairwise distances are corrupted by independent additive Gaussian noise. This formulation yields a stress objective function, derived from an explicit probabilistic model, allowing for a rigorous statistical analysis. Up to rotations and translations, we also prove the consistency of the estimator when the noise vanishes and prove finite-sample probability bounds on the estimation error. Our results complement the recently developed theories by focusing on a fixed size of data with increasingly accurate distance measurements.