Analysis of dynamic metabolomics data sets holds the promise to improve our understanding of the underlying mechanisms in human metabolism. That is crucial to detect the changes in the metabolism that can potentially lead to diseases. Dynamic metabolomics data has more than two axes of variation, i.e., samples, metabolites and time. While such time-evolving multi-way data sets are collected more and more in recent years, revealing the underlying mechanisms and their dynamics from such data remains challenging. 

This talk will focus on a systematic study demonstrating the advantages and limitations of multi-way data analysis (also known as tensor factorizations) in terms of analyzing dynamic metabolomics data. We study different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, a human cholesterol model, and generate data with different types of variation. Our numerical experiments demonstrate that despite the increasing complexity of the studied models, tensor factorization methods CANDECOMP/PARAFAC(CP) and PARAllel Profiles with LINear Dependences (PARALIND) can reveal the underlying mechanisms and their dynamics.