Model-coupled autoencoder for time series visualisation

Abstract

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.

An explorative approach for inspectingKeplerdata

“…We mention in passing that the parameter configuration used for the proposed method was an ESN with a hidden reservoir of 50 neurons using the cycle architecture (Rodan & Tiňo 2012) coupled to an autoencoder with a hidden layer of 10 neurons. More information on the parameters, can be found in Gianniotis et al (2015). For the plain autoencoder, we also used a hidden layer of 10 neurons.…”

“…A more detailed account of the adopted methodology in this work has previously appeared in Gianniotis et al (2015). The terms time-series and sequence are used interchangeably.…”

“…φ encodes various aspects of the neural network architecture of the ESN (number of neurons h, connectivity, weight structure, etc.) which we do not discuss here; instead we refer the interested reader to Gianniotis et al (2015) and references therein.…”

“…A better measure would be to check how well the reconstructioñ w still represents its corresponding sequence y. This can be simply checked by looking at the reconstruction error y − Φw 2 measured with respect to the sequence y, as proposed in Gianniotis et al (2015). This measure is much more meaningful as it measures reconstruction in terms of the prediction quality of the underlying ESN model.…”

Diverse Relevance Feedback for Time Series with Autoencoder Based Summarizations

“…It has attracted a renewed interest lately with deep network approaches generally utilizing restricted Boltzmann machines [35]. There has been recent work done on time series visualization utilizing autoencoder structures [36]. Time series forecasting with neural networks is reported to be advantageous even with relatively small data cases [37].…”