In this work, we present a novel method for hierarchically variable clustering using singular value decomposition. Our proposed approach provides a non-parametric solution to identify block diagonal patterns in covariance (correlation) matrices, thereby grouping variables according to their dissimilarity. We explain the methodology and outline the incorporation of linkage functions to assess dissimilarities between clusters. To validate the efficiency of our method, we perform both a simulation study and an analysis of real-world data. Our findings show the approach's robustness. We conclude by discussing potential extensions and future directions for research in this field. Supplementary materials for this article can be accessed online.

翻译：本文提出了一种利用奇异值分解进行层次变量聚类的新方法。该方法提供了一种非参数解，用于识别协方差（相关）矩阵中的块对角模式，从而根据变量的相异度对其进行分组。我们阐述了该方法的原理，并概述了如何引入连接函数来评估聚类之间的相异度。为验证该方法的有效性，我们进行了模拟研究与真实数据分析，结果证明了该方法的稳健性。最后，我们讨论了该领域潜在的扩展方向与未来研究路径。本文的补充材料可在线获取。