kNN Ensembles with Penalized DTW for Multivariate Time Series Imputation

The imputation of partially missing multivariate time series data is critical for its correct analysis. The biggest problems in time series data are consecutively missing values that would result in serious information loss if simply dropped from the dataset. To address this problem, we adapt the k-Nearest Neighbors algorithm in a novel way for multivariate time series imputation. The algorithm employs Dynamic Time Warping as distance metric instead of pointwise distance measurements. We preprocess the data with linear interpolation to create complete windows for Dynamic Time Warping. The algorithm derives global distance weights from the correlation between features and consecutively missing values are penalized by individual distance weights to reduce error transfer from linear interpolation. Finally, efficient ensemble methods improve the accuracy. Experimental results show accurate imputations on datasets with a high correlation between features. Further, our algorithm shows better results with consecutively missing values than state-of-the-art algorithms.