Gaussian process clustering for the functional characterisation of vital-sign trajectories

Recognition of complex trajectories in multivariate time-series data requires effective models and representations for the analysis and matching of functional data. In this work, we introduce a new representation that allows for matching of noisy, and unevenly-sampled trajectories, and we explore whether this representation may be used to characterise the state of health of a patient based on vital-sign data. We model the evolution of each vital-sign trajectory using multivariate Gaussian process regression, and we introduce a similarity measurement for the comparison of latent functions based on the local likelihood of the points in each trajectory. The similarity measurement is then used for recognising known trajectories and identifying unknown trajectories as would be required for identifying “abnormal” vital-sign time-series. We test our approach using a dataset that contains vital-sign observational data collected from a cohort of 154 patients who are recovering from gastrointestinal surgery. We show that our approach is able to discriminate between abnormal patient trajectories corresponding to those who deteriorated physiologically and were admitted to a higher level of care, from those belonging to patients who had no clinically relevant events.