An empirical comparison of resolution methods for three-way arrays

Abstract In chemometrics applications it is common to resolve a trilinear array by solving a generalized eigenvalue problem, rather than by employing the iterative PARAFAC algorithm commonly used by psychometricians. Although an eigenanalysis-based procedure works perfectly in the absence of noise, it is not guaranteed to yield least squares resolutions when noise is present. The PARAFAC algorithm on the other hand is guaranteed to reduce the residual sum of squares at each iteration. In this paper we propose synthesizing the two methods by using the resolution generated by eigenanalysis as starting values for the iterative PARAFAC algorithm. We find for simulated four-component data at moderate noise levels that following an eigenanalysis resolution with PARAFAC frequently leads to significant improvement in the quality of the resolution.