On rotational ambiguity in parallel factor analysis

An aspect which is significantly less documented in the previous publications is the reliable detection of rotational ambiguities in multi-way methods. A few reported methods are based on bilinear models for calculating the feasible bands of three-way data. In this paper we propose a method to calculate feasible bands of resolved profiles of components in three-way methods and visualize the rotational ambiguity in three-way data in the results of the three-way methods. Most of discussion is in the PARAFAC algorithm. The principle behind the algorithm is described in detail and tested for simulated data set. Completely general and exhaustive results are presented for the two-component cases. In particular, the effect of the noise is investigated and a comparison is made between feasible solutions obtained from PARAFAC and matrix-augmented with trilinearity. It is shown that the results obtained from both methods are identical.