Model-Coupled Autoencoder for Time Series Visualisation
  We present an approach for the visualisation of a set of time series that combines an echo state network with an autoencoder. For each time series in the dataset we train an echo state network, using a common and fixed reservoir of hidden neurons, and use the optimised readout weights as the new representation. Dimensionality reduction is then performed via an autoencoder on the readout weight representations. The crux of the work is to equip the autoencoder with a loss function that correctly interprets the reconstructed readout weights by associating them with a reconstruction error measured in the data space of sequences. This essentially amounts to measuring the predictive performance that the reconstructed readout weights exhibit on their corresponding sequences when plugged back into the echo state network with the same fixed reservoir. We demonstrate that the proposed visualisation framework can deal both with real valued sequences as well as binary sequences. We derive magnification factors in order to analyse distance preservations and distortions in the visualisation space. The versatility and advantages of the proposed method are demonstrated on datasets of time series that originate from diverse domains. 
Nikolaos Gianniotis and Sven D. K\"ugler and Peter Ti\v{n}o and Kai L.   Polsterer
astro-ph.IM cs.NE