On the Use of Dictionary Learning in Time Series Imputation

In this work, we show how dictionary learning (DL) can be employed in the imputation of univariate and multivariate time series. In the multivariate case, we propose to use a structured dictionary. The size of the dictionary and the sparsity level are selected by information theoretic criteria. We also evaluate the effect of removing the trend/seasonality before applying DL. We conduct an extensive experimental study on real-life data. The positions of the missing data are simulated by applying two strategies: (i) sampling without replacement, which leads to isolated occurrences of the missing data, and (ii) sampling via Polya urn model that is likely to produce long sequences of missing data. In all scenarios, the novel DL-based methods compare favorably with the state-of-the-art.