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Analyzing multi-way measurements with variations across one mode of thedataset is a challenge in various fields including data mining, neuroscienceand chemometrics. For example, measurements may evolve over time or haveunaligned time profiles. The PARAFAC2 model has been successfully used toanalyze such data by allowing the underlying factor matrices in one mode (i.e.,the evolving mode) to change across slices. The traditional approach to fit aPARAFAC2 model is to use an alternating least squares-based algorithm, whichhandles the constant cross-product constraint of the PARAFAC2 model byimplicitly estimating the evolving factor matrices. This approach makesimposing regularization on these factor matrices challenging. There iscurrently no algorithm to flexibly impose such regularization with generalpenalty functions and hard constraints. In order to address this challenge andto avoid the implicit estimation, in this paper, we propose an algorithm forfitting PARAFAC2 based on alternating optimization with the alternatingdirection method of multipliers (AO-ADMM). With numerical experiments onsimulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows forflexible constraints, recovers the underlying patterns accurately, and iscomputationally efficient compared to the state-of-the-art. We also apply ourmodel to two real-world datasets from neuroscience and chemometrics, and showthat constraining the evolving mode improves the interpretability of theextracted patterns.

An AO-ADMM approach to constraining PARAFAC2 on all modes