  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.
