Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data

Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust \emph{time series cluster kernel} (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.Comment: 23 pages, 6 figure

Time series kernel similarities for predicting Paroxysmal Atrial Fibrillation from ECGs

We tackle the problem of classifying Electrocardiography (ECG) signals with the aim of predicting the onset of Paroxysmal Atrial Fibrillation (PAF). Atrial fibrillation is the most common type of arrhythmia, but in many cases PAF episodes are asymptomatic. Therefore, in order to help diagnosing PAF, it is important to design procedures for detecting and, more importantly, predicting PAF episodes. We propose a method for predicting PAF events whose first step consists of a feature extraction procedure that represents each ECG as a multi-variate time series. Successively, we design a classification framework based on kernel similarities for multi-variate time series, capable of handling missing data. We consider different approaches to perform classification in the original space of the multi-variate time series and in an embedding space, defined by the kernel similarity measure. We achieve a classification accuracy comparable with state of the art methods, with the additional advantage of detecting the PAF onset up to 15 minutes in advance

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

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 method

A Kernel to Exploit Informative Missingness in Multivariate Time Series from EHRs

A large fraction of the electronic health records (EHRs) consists of clinical measurements collected over time, such as lab tests and vital signs, which provide important information about a patient's health status. These sequences of clinical measurements are naturally represented as time series, characterized by multiple variables and large amounts of missing data, which complicate the analysis. In this work, we propose a novel kernel which is capable of exploiting both the information from the observed values as well the information hidden in the missing patterns in multivariate time series (MTS) originating e.g. from EHRs. The kernel, called TCK$_{IM}$, is designed using an ensemble learning strategy in which the base models are novel mixed mode Bayesian mixture models which can effectively exploit informative missingness without having to resort to imputation methods. Moreover, the ensemble approach ensures robustness to hyperparameters and therefore TCK$_{IM}$ is particularly well suited if there is a lack of labels - a known challenge in medical applications. Experiments on three real-world clinical datasets demonstrate the effectiveness of the proposed kernel.Comment: 2020 International Workshop on Health Intelligence, AAAI-20. arXiv admin note: text overlap with arXiv:1907.0525

Learning representations of multivariate time series with missing data

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordLearning compressed representations of multivariate time series (MTS) facilitates data analysis in the presence of noise and redundant information, and for a large number of variates and time steps. However, classical dimensionality reduction approaches are designed for vectorial data and cannot deal explicitly with missing values. In this work, we propose a novel autoencoder architecture based on recurrent neural networks to generate compressed representations of MTS. The proposed model can process inputs characterized by variable lengths and it is specifically designed to handle missing data. Our autoencoder learns fixed-length vectorial representations, whose pairwise similarities are aligned to a kernel function that operates in input space and that handles missing values. This allows to learn good representations, even in the presence of a significant amount of missing data. To show the effectiveness of the proposed approach, we evaluate the quality of the learned representations in several classification tasks, including those involving medical data, and we compare to other methods for dimensionality reduction. Successively, we design two frameworks based on the proposed architecture: one for imputing missing data and another for one-class classification. Finally, we analyze under what circumstances an autoencoder with recurrent layers can learn better compressed representations of MTS than feed-forward architectures.Norwegian Research Counci