Time Series Averaging Using Multi-Tasking Autoencoder

The estimation of an optimal time series average has been studied for over three decades. The process is mainly challenging due to temporal distortion. Previous approaches mostly addressed this challenge by using alignment algorithms such as Dynamic Time Warping (DTW). However, the quadratic computational complexity of DTW and its inability to align more than two time series simultaneously complicate the estimation. In this paper, we follow a different path and state the averaging problem as a generative problem. To this end, we propose a multi-tasking convolutional autoencoder architecture to extract latent features of similarly labeled time series under the influence of temporal distortion. We then take the arithmetic mean of latent features as an estimate of the latent mean. Moreover, we project these estimations and investigate their performance in the time domain. We evaluated the proposed approach through one nearest centroid classification using 85 data sets obtained from the UCR archive. Experimental results show that, in the latent space, the proposed multi-tasking autoencoder achieves competitive accuracies as compared to the state-of-the-art, thus demonstrating that the learned latent space is suitable to compute time series averages. In addition, the time domain projection of latent space means provides superior results as compared to time domain arithmetic means.