On varimax asymptotics in network models and spectral methods for dimensionality reduction
本文在Rohe & Zeng (2023)基础上，证明最大方差旋转与谱截断结合时，在潜变量模型中能进行统计估计，并建立低维节点嵌入向量的渐近多元正态性，涉及网络稀疏性、数据去噪和矩阵秩的作用。
Abstract Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by Kaiser (1958), have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by Rohe & Zeng (2023) 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 new-found 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.