  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. Our experiments
demonstrate that SLAC-Time outperforms the baseline K-means clustering
algorithm in terms of silhouette coefficient, Calinski Harabasz index, Dunn
index, and Davies Bouldin index. 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.
