Clusterwise Non-negative Matrix Factorization (NMF) for capturing variability in time profiles

Clusterwise Non-negative Matrix Factorization (NMF) for capturing variability in time profiles In many domains, researchers are interested in capturing variability in time profiles. For example in emotion research, the time dynamics of emotions is a hot topic; hence, researchers recently have started gathering data on the intensity of different emotion components (e.g., appraisals, physiological features, subjective experience) at several time points during an emotion episode. These intensity profiles of emotional episodes and intra- and interindividual differences therein are an interesting aspect of the time dynamics of emotions. To capture the variability in such profiles, one can use functional component analysis or K-means clustering. Both strategies have some advantages but also some drawbacks. We propose a new method that combines the attractive features of these two strategies: Clusterwise Non-negative Matrix Factorization (NMF). This methods assigns observations (e.g., emotional episodes, persons) into clusters according to the associated time profiles. The profiles within each cluster are decomposed into a general profile and an intensity score per observation that indicates the intensity of the general profile for specific observations. As Clusterwise NMF model is closely related to Mixtures of Factor Analyzers, we will discuss the similarities and differences of both methods. Finally, we will apply Clusterwise NMF to intensity profiles of emotional episodes.status: publishe