Traumatic Brain Injury (TBI) presents a broad spectrum of clinical presentations and outcomes due to its inherent heterogeneity, leading to diverse recovery trajectories and varied therapeutic responses. While many studies have delved into TBI phenotyping for distinct patient populations, identifying TBI phenotypes that consistently generalize across various settings and populations remains a critical research gap. Our research addresses this by employing multivariate time-series clustering to unveil TBI's dynamic intricates. Utilizing a self-supervised learning-based approach to clustering multivariate time-Series data with missing values (SLAC-Time), we analyzed both the research-centric TRACK-TBI and the real-world MIMIC-IV datasets. Remarkably, the optimal hyperparameters of SLAC-Time and the ideal number of clusters remained consistent across these datasets, underscoring SLAC-Time's stability across heterogeneous datasets. Our analysis revealed three generalizable TBI phenotypes ({\alpha}, \b{eta}, and {\gamma}), each exhibiting distinct non-temporal features during emergency department visits, and temporal feature profiles throughout ICU stays. Specifically, phenotype {\alpha} represents mild TBI with a remarkably consistent clinical presentation. In contrast, phenotype \b{eta} signifies severe TBI with diverse clinical manifestations, and phenotype {\gamma} represents a moderate TBI profile in terms of severity and clinical diversity. Age is a significant determinant of TBI outcomes, with older cohorts recording higher mortality rates. Importantly, while certain features varied by age, the core characteristics of TBI manifestations tied to each phenotype remain consistent across diverse populations.

Self-supervised learning approaches provide a promising direction for clustering multivariate time-series data. However, real-world time-series data often include missing values, and the existing approaches require imputing missing values before clustering, which may cause extensive computations and noise and result in invalid interpretations. To address these challenges, we present a Self-supervised Learning-based Approach to Clustering multivariate Time-series data with missing values (SLAC-Time). SLAC-Time is a Transformer-based clustering method that uses time-series forecasting as a proxy task for leveraging unlabeled data and learning more robust time-series representations. This method jointly learns the neural network parameters and the cluster assignments of the learned representations. It iteratively clusters the learned representations with the K-means method and then utilizes the subsequent cluster assignments as pseudo-labels to update the model parameters. To evaluate our proposed approach, we applied it to clustering and phenotyping Traumatic Brain Injury (TBI) patients in the Transforming Research and Clinical Knowledge in Traumatic Brain Injury (TRACK-TBI) study. Clinical data associated with TBI patients are often measured over time and represented as timeseries variables characterized by missing values and irregular time intervals. We identified three TBI phenotypes that are distinct from one another in terms of clinically significant variables as well as clinical outcomes, including the Extended Glasgow Outcome Scale (GOSE) score, Intensive Care Unit (ICU) length of stay, and mortality rate. The experiments show that the TBI phenotypes identified by SLAC-Time can be potentially used for developing targeted clinical trials and therapeutic strategies. Keywords Self-supervised learning; Clustering; Transformer; Multivariate time-series data; Traumatic brain injury 1. Introduction Multivariate time-series data are frequently observed in many healthcare domains where each patient is represented by a set of clinical measurements recorded over time and present important information spanning the whole course of a patient's care. Clustering approaches are commonly used to extract valuable information and patterns from multivariate time-series data [1]. Such clustering approaches can be broadly divided into two categories: raw data-based approaches and representation-based approaches [2]. Raw data-based approaches perform the clustering on raw input data using well-designed similarity measures that can address the specificities of the temporal dimension, including shifted or stretched patterns (e.g., [3-5]).