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

• Published in: Pattern recognition Vol. 115; p. 107896
• Main Authors: Øyvind Mikalsen, Karl, Soguero-Ruiz, Cristina, Maria Bianchi, Filippo, Revhaug, Arthur, Jenssen, Robert
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2021; Elsevier
• Subjects: Fysikk: 430; Informative missingness; Kernel methods; Matematikk og Naturvitenskap: 400; Mathematics and natural science: 400; Missing data; Multivariate time series; Physics: 430; Semi-supervised learning; VDP; Informative missingness; Kernel methods; Missing data; Multivariate time series; Semi-supervised learning
• ISSN: 0031-3203; 1873-5142; 1873-5142
• DOI: 10.1016/j.patcog.2021.107896

•Two novel kernels for multivariate time series with missing data are proposed.•Informative missingness is exploited using mixed mode Bayesian mixture models.•We exploit incomplete label information using ideas from information theory.•A case study of patients suffering from infectious postoperative complications. The time series cluster kernel (TCK) provides a powerful tool for analysing multivariate time series subject to missing data. TCK is designed using an ensemble learning approach in which Bayesian mixture models form the base models. Because of the Bayesian approach, TCK can naturally deal with missing values without resorting to imputation and the ensemble strategy ensures robustness to hyperparameters, making it particularly well suited for unsupervised learning. However, TCK assumes missing at random and that the underlying missingness mechanism is ignorable, i.e. uninformative, an assumption that does not hold in many real-world applications, such as e.g. medicine. To overcome this limitation, we present a kernel capable of exploiting the potentially rich information in the missing values and patterns, as well as the information from the observed data. In our approach, we create a representation of the missing pattern, which is incorporated into mixed mode mixture models in such a way that the information provided by the missing patterns is effectively exploited. Moreover, we also propose a semi-supervised kernel, capable of taking advantage of incomplete label information to learn more accurate similarities. Experiments on benchmark data, as well as a real-world case study of patients described by longitudinal electronic health record data who potentially suffer from hospital-acquired infections, demonstrate the effectiveness of the proposed methods.