Orthogonal Procrustes problem

• https://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem

The problem of finding the best rotation ($\Omega$) that matches two sets of vectors $A$ and $B$:

$$R = \arg\min_\Omega\|\Omega A-B\|_F \quad\mathrm{subject\ to}\quad \Omega^T \Omega=I$$

Schönemann1966generalized provides a generalized solution.

The problem of aligning Word embedding (or any Embedding) across different snapshots (e.g., Hamilton2016diachronic).