Learning representations for multivariate time series with missing data using Temporal Kernelized Autoencoders

Learning compressed representations of multivariate time series (MTS) facilitate the analysis and process of the data in presence of noise, redundant information, and large amount of variables and time steps. However, classic dimensionality reduction approaches are not designed to process sequential data, especially in the presence of missing values. In this work, we propose a novel autoencoder architecture based on recurrent neural networks to generate compressed representations of MTS, which may contain missing values and have variable lengths. Our autoencoder learns fixed-length vectorial representations, whose pairwise similarities are aligned with a kernel function that operates in input space and handles missing values. This, allows to preserve relationships in the low-dimensional vector space even in presence of missing values. To highlight the main features of the proposed autoencoder, we first investigate its performance in controlled experiments. Successively, we show how the learned representations can be exploited both in several benchmark and real-world classification tasks on medical data. Finally, based on the proposed architecture, we conceive a framework for one-class classification and imputation of missing data in time series extracted from ECG signals.