  Learning compressed representations of multivariate time series (MTS)
facilitates data analysis in the presence of noise and redundant information,
and for a large number of variates and time steps. However, classical
dimensionality reduction approaches are designed for vectorial data and cannot
deal explicitly with missing values. In this work, we propose a novel
autoencoder architecture based on recurrent neural networks to generate
compressed representations of MTS. The proposed model can process inputs
characterized by variable lengths and it is specifically designed to handle
missing data. Our autoencoder learns fixed-length vectorial representations,
whose pairwise similarities are aligned to a kernel function that operates in
input space and that handles missing values. This allows to learn good
representations, even in the presence of a significant amount of missing data.
To show the effectiveness of the proposed approach, we evaluate the quality of
the learned representations in several classification tasks, including those
involving medical data, and we compare to other methods for dimensionality
reduction. Successively, we design two frameworks based on the proposed
architecture: one for imputing missing data and another for one-class
classification. Finally, we analyze under what circumstances an autoencoder
with recurrent layers can learn better compressed representations of MTS than
feed-forward architectures.
