An analysis of classical multidimensional scaling with applications to clustering
An analysis of classical multidimensional scaling with applications to clustering
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DOI：
10.1093/imaiai/iaac004
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发表时间：
2022-04-23
影响因子：
1.6
通讯作者：
Sun，Qiang
中科院分区：
文献类型：
--
作者：
Little，Anna;Xie，Yuying;Sun，Qiang
经典多维缩放是一种广泛使用的降维技术。然而，描述其统计性能的理论结果却很少。本文为分析经典多维尺度生成的嵌入样本的质量提供了一个理论框架。这为各种下游统计分析奠定了基础，我们专注于对噪声数据进行聚类。我们的结果提供了信噪比的缩放条件，在该条件下，经典的多维缩放和基于距离的聚类算法可以恢复所有样本的聚类标签。模拟研究证实这些缩放条件是尖锐的。癌症基因表达数据、单细胞RNA测序数据和自然语言数据的应用为方法和理论提供了强有力的支持。
Classical multidimensional scaling is a widely used dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays a foundation for various downstream statistical analyses, and we focus on clustering noisy data. Our results provide scaling conditions on the signal-to-noise ratio under which classical multidimensional scaling followed by a distance-based clustering algorithm can recover the cluster labels of all samples. Simulation studies confirm these scaling conditions are sharp. Applications to the cancer gene-expression data, the single-cell RNA sequencing data and the natural language data lend strong support to the methodology and theory.