Two-mode K-spectral centroid analysis for studying multivariate longitudinal profiles

In many scientific areas, researchers collect multivariate time profile data on the evolution of a set of variables across time for multiple persons. For instance, clinical studies often focus on the effects of an intervention on different symptoms for multiple persons, by repeatedly measuring symptom severity for each symptom and each person. To pursue an insightful overview on how these time profiles vary as a function of both symptoms and persons, we propose two-mode K-Spectral Centroid (2M-KSC) analysis, which is a multivariate extension of K-Spectral Centroid analysis. Specifically, 2M-KSC assigns the persons to a few person clusters and the symptoms to a few symptom clusters and imposes that the time profiles that correspond to a specific combination of a person cluster and a symptom cluster have the same shape, but may vary in amplitude scaling. An algorithm for fitting 2M-KSC is proposed and evaluated in a simulation study. Finally, the new method is applied to time profiles regarding the severity of depression symptoms during a citalopram treatment.