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The time series cluster kernel (TCK) provides a powerful tool for analysingmultivariate time series subject to missing data. TCK is designed using anensemble learning approach in which Bayesian mixture models form the basemodels. Because of the Bayesian approach, TCK can naturally deal with missingvalues without resorting to imputation and the ensemble strategy ensuresrobustness to hyperparameters, making it particularly well suited forunsupervised learning.  However, TCK assumes missing at random and that the underlying missingnessmechanism is ignorable, i.e. uninformative, an assumption that does not hold inmany real-world applications, such as e.g. medicine. To overcome thislimitation, we present a kernel capable of exploiting the potentially richinformation in the missing values and patterns, as well as the information fromthe observed data. In our approach, we create a representation of the missingpattern, which is incorporated into mixed mode mixture models in such a waythat the information provided by the missing patterns is effectively exploited.Moreover, we also propose a semi-supervised kernel, capable of taking advantageof incomplete label information to learn more accurate similarities.  Experiments on benchmark data, as well as a real-world case study of patientsdescribed by longitudinal electronic health record data who potentially sufferfrom hospital-acquired infections, demonstrate the effectiveness of theproposed methods.

Time series cluster kernels to exploit informative missingness and incomplete label information