rv-coefficient-equals-linear-cka-on-centered-data
IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-1.md
Created 2026-08-24T17:10:50+00:00
The RV coefficient computed on centered representations is algebraically identical to linear CKA (CKA_lin(X,Y) = ‖X_cᵀY_c‖²_F / (‖X_cᵀX_c‖_F · ‖Y_cᵀY_c‖_F)), differing only in historical motivation and in the uncentered case.
Summary
On centered data, the RV coefficient and linear CKA are the same number computed two different ways, so any comparison or threshold you set with one automatically applies to the other. This means the system does not need to track them as separate metrics when representations are centered; they reduce to a single measurement of how well two sets of features align.