Probabilistic PARAFAC2
This work addresses a problem for researchers analyzing multi-way data with incomparable units, offering incremental improvements in robustness and uncertainty handling.
The paper tackled the challenge of making PARAFAC2, a multimodal factor analysis model for multi-way data, more robust to noise and better at determining factor numbers by developing a probabilistic formulation. The result showed improved robustness to noise and model order misspecification on simulated and real data, though no specific numerical gains were provided.
The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable in order to improve robustness to noise and provide a well founded principle for determining the number of factors, but challenging because the factor loadings are constrained to be orthogonal. We develop two probabilistic formulations of the PARAFAC2 along with variational procedures for inference: In the one approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the other, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulation to the conventional direct fitting algorithm based on maximum likelihood. On simulated data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data, we compare our approach to the conventional PARAFAC2 model estimation and find that the probabilistic formulation is more robust to noise and model order misspecification. The probabilistic PARAFAC2 thus forms a promising framework for modeling multi-way data accounting for uncertainty.