Multivariate Time Series as Images: Imputation Using Convolutional Denoising Autoencoder

Abstract

Missing data is a common occurrence in the time series domain, for instance due to faulty sensors, server downtime or patients not attending their scheduled appointments. One of the best methods to impute these missing values is Multiple Imputations by Chained Equations (MICE) which has the drawback that it can only model linear relationships among the variables in a multivariate time series. The advancement of deep learning and its ability to model non-linear relationships among variables make it a promising candidate for time series imputation. This work proposes a modified Convolutional Denoising Autoencoder (CDA) based approach to impute multivariate time series data in combination with a preprocessing step that encodes time series data into 2D images using Gramian Angular Summation Field (GASF). We compare our approach against a standard feed-forward Multi Layer Perceptron (MLP) and MICE. All our experiments were performed on 5 UEA MTSC multivariate time series datasets, where 20 to 50% of the data was simulated to be missing completely at random. The CDA model outperforms all the other models in 4 out of 5 datasets and is tied for the best algorithm in the remaining case.