Getting to the core of PARAFAC2, a nonnegative approach

This work presents a novel method of performing PARAFAC2 factorization of three-way data using a compact representation of that data. In the standard PARAFAC2 algorithm, two modes of the data are recovered directly during the decomposition while the third mode is returned as a transformation matrix, which is then used to rotate sets of orthogonal third-mode basis factors into interpretable factors. In our new method, the data are first decomposed into a core matrix and orthogonal factor loading matrices in the first two modes as well as sets of orthogonal factors in the third mode (as in standard PARAFAC2). The core matrix is then decomposed using a the standard PARAFAC2 strategy to produce transformation matrices in all three modes. The algorithm is particularly useful for very large data sets and essentially permits imposition of nonnegativity in all three modes. •Fast method for performing PARAFAC2 decompositions.•Permits imposition of nonnegativity in all three modes.•Novel application of compression for three-way factor analysis.