Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by H. Kaiser, have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by K. Rohe and M. Zeng provides new, fundamental insight: varimax rotations provably perform statistical estimation in certain classes of latent variable models when paired with spectral-based matrix truncations for dimensionality reduction. We build on this newfound understanding of varimax rotations by developing further connections to network analysis and spectral methods rooted in entrywise matrix perturbation analysis. Concretely, this paper establishes the asymptotic multivariate normality of vectors in varimax-transformed Euclidean point clouds that represent low-dimensional node embeddings in certain latent space random graph models. We address related concepts including network sparsity, data denoising, and the role of matrix rank in latent variable parameterizations. Collectively, these findings, at the confluence of classical and contemporary multivariate analysis, reinforce methodology and inference procedures grounded in matrix factorization-based techniques. Numerical examples illustrate our findings and supplement our discussion.

翻译：自H. Kaiser提出以来，变分极大因子旋转虽然在心理学和统计学实践者中广受欢迎，但历来受到部分理论学家和数理统计学家的质疑与怀疑。如今，K. Rohe与M. Zeng的研究提供了全新的基础性见解：当与基于谱的矩阵截断降维方法结合时，变分极大旋转在特定潜在变量模型类别中可证明地实现统计估计。我们在这一对变分极大旋转的新理解基础上，进一步发展其与网络分析及基于元素矩阵扰动分析的谱方法之间的关联。具体而言，本文建立了在特定潜在空间随机图模型中代表低维节点嵌入的变分极大变换欧几里得点云中向量的渐近多元正态性。我们探讨了相关概念，包括网络稀疏性、数据去噪以及矩阵秩在潜在变量参数化中的作用。总体而言，这些处于经典与当代多元分析交汇处的发现，强化了基于矩阵分解技术的统计方法和推断程序。数值算例展示了我们的发现并对讨论进行了补充。