This paper links multiple invariance sensor array processing (MI-SAP) to pa
rallel factor (PARAFAC) analysis, which is a tool rooted in psychometrics a
nd chemometrics. PARAFAC is a common name for low-rank decomposition of thr
ee- and higher way arrays. This link facilitates the derivation of powerful
identifiability results for MI-SAP, shows that the uniqueness of single- a
nd multiple-invariance ESPRIT stems from uniqueness-of low-rank decompositi
on of three-way arrays, and allows tapping on the available expertise for f
itting the PARAFAC model. The results are applicable to both data-domain an
d subspace MI-SAP formulations. The paper also includes a constructive uniq
ueness proof for a special PARAFAC model.