Hidden dynamic learning for long-interval consecutive missing values reconstruction in EEG time series

Accurate and reliable estimation of multiple coevolving time series over random long-interval consecutive missing values have become the new frontier of the reconstruction discipline. If the problem of missing values cannot be solved, a significant number of important data sets will be improperly analyzed or discarded as they can distort and repudiate the usage of several methodologies. Conventional interpolation approaches are commonly used to estimate missing values in incomplete time series patterns. However, these methods are ignoring the correlations among multiple dimensions and becoming invalid for long period of missing values. This research therefore proposes a new approach to automatically recover missing values based on applying Linear Dynamical System. The proposed approach captures correlations between multiple coevolving time sequences via identifying a few hidden variables and mining their dynamics to impute missing values. The proposed methodology recovers random consecutive observation of the missing values with low reconstruction errors. Moreover, the proposed method offers a robust and scalable approach with linear computation time over the size of sequences. The proposed method´s applicability is demonstrated on real world electroencephalogram (EEG) signals where incomplete data frequently occur due to corrupted transmission of equipment electrodes.