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A Framework for Clinical Classification of Multivariate Time Series using Koopman Operators
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Yakir Yehuda
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Sunday, 04.09.2022, 11:00
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Zoom Lecture: 2488049770
Clinical multivariate time series (MTS) arising from sensor data, such as EEG and ECG, is used in a variety of tasks. The sensors are composed of multiple leads connected to the body, where each lead generates a time series of data. Combining information from the different leads allows inference of cardiac activity from ECG (arrhythmia, acute coronary syndrome) or brain dysfunction from EEG (brain tumors, strokes, epilepsy). We present a framework for clinical classification of MTS based on their joint dynamics. Specifically, we learn a dynamical system describing the evolution of the multiple signals together in time based on the theory of Koopman operators. According to Koopman theory, a high-dimensional embedding space exists in which the operator propagating from one time instant to the next is linear; thus, we learn both the mapping to this embedding space and the linear operator that corresponds to it. We then pose a joint optimization framework and learn the linear MTS dynamics, while simultaneously optimizing the loss corresponding to the original classification task, where classification depends on the Koopman embedding. Our technique yields reliable clinical diagnosis in an empirical study employing signals from thousands of patients in multiple clinical tasks employing two types of clinical-grade sensors (ECG and EEG).