“…To preserve the multiway structure of time-resolved data, recent work arranges postprandial data as a third-order tensor with modes: subjects, metabolites, and time, and use tensor factorizations, i.e., extensions of matrix factorizations to multiway arrays (Smilde et al, 2004;Acar and Yener, 2009;Kolda and Bader, 2009), to reveal the underlying patterns in subjects, metabolites and time modes (Li et al, 2023;Yan et al, 2023;Fujita et al, 2023). For instance, Li et al use the CANDECOMP/PARAFAC (CP) (Harshman, 1970;Carroll and Chang, 1970) tensor model to analyze simulated challenge test data generated by a human whole-body metabolic model, and demonstrate that the analysis of fasting signals (i.e., T 0 data) using PCA and the analysis of dynamic data (i.e., T 0 -corrected data obtained by subtracting fasting signals from postprandial data) using CP reveal metabolic differences at fasting vs. dynamic states (Li et al, 2023).…”