Evaluating multivariate time-series clustering using simulated ecological momentary assessment data

During an Ecological Momentary Assessment (EMA) study, through repeated digital questionnaires, we have the opportunity to collect multiple multivariate time-series (MTS) data for all participants. Although, it is common that individual data is analyzed per participant, the richness of such dataset poses the question of whether meaningful groups of individuals could be uncovered to better understand the underlying processes on an individual and a group level. Such grouping could be obtained by clustering. Therefore, this paper examines the performance of various clustering approaches for grouping individuals based on the similarity of their raw time-series data patterns. Clustering is an unsupervised task, where the true underlying groups are not usually available, making the result difficult to evaluate. Therefore, in the current paper, simulated irregular time-series data, resembling EMA, are used to validate the performance of several methods under different clustering-related choices, such as the distance metric. Data are generated with a varying number of clusters, total number of individuals and time-points as well as number of variables and proportions of noisy variables, while their time-series represent well-shaped patterns, typically observed in emotional behavior. After applying clustering to all simulated datasets, clustering performance was first assessed by comparing the true and predicted labels, while the impact of the different datasets’ parameters was also examined. Because ground truth labels are not always available, or do not even exist, in real-world scenarios, clustering evaluation through distance-based and distance-free measures was further investigated. Overall, all clustering methods (e.g. k-means, Hierarchical clustering, Fuzzy k-medoids) proved reliable in different configurations, revealing the true number of clusters. Moreover, kernel-based methods appeared more efficient when highly noisy variables are involved, becoming more promising for real-world data. As a second part, an illustration of two specific simulated scenarios (datasets) is provided, showing, in more detail, all different analysis steps before drawing a conclusion about the choice of the optimal number of clusters.