Statistical Significance of Clustering with Multidimensional Scaling
针对传统聚类显著性检验方法在高维小样本数据中的局限，以及仅能获取相异矩阵的场景，提出一种基于多维尺度分析的新方法，通过降维后检验聚类显著性，模拟和实际数据验证效果良好。
Clustering is a fundamental tool for exploratory data analysis. One central problem in clustering is deciding if the clusters discovered by clustering methods are reliable as opposed to being artifacts of natural sampling variation. Statistical significance of clustering (SigClust) is a recently developed cluster evaluation tool for high-dimension, low-sample size data. Despite its successful application to many scientific problems, there are cases where the original SigClust may not work well. Furthermore, for specific applications, researchers may not have access to the original data and only have the dissimilarity matrix. In this case, clustering is still a valuable exploratory tool, but the original SigClust is not applicable. To address these issues, we propose a new SigClust method using multidimensional scaling (MDS). The underlying idea behind MDS-based SigClust is that one can achieve low-dimensional representations of the original data via MDS using only the dissimilarity matrix and then apply SigClust on the low-dimensional MDS space. The proposed MDS-based SigClust can circumvent the challenge of parameter estimation of the original method in high-dimensional spaces while keeping the essential clustering structure in the MDS space. Both simulations and real data applications demonstrate that the proposed method works remarkably well for assessing the statistical significance of clustering. Supplemental materials for the article are available online.