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dc.contributor.authorBianchi, FM
dc.contributor.authorLivi, L
dc.contributor.authorAlippi, C
dc.date.accessioned2017-03-01T16:38:48Z
dc.date.issued2016-12-02
dc.description.abstractIn this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called Lmax, is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem.en_GB
dc.identifier.citationPublished online 02 December 2016en_GB
dc.identifier.doi10.1109/TNNLS.2016.2630802
dc.identifier.urihttp://hdl.handle.net/10871/26176
dc.language.isoenen_GB
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en_GB
dc.relation.urlhttps://www.ncbi.nlm.nih.gov/pubmed/28114039en_GB
dc.subjectReservoirsen_GB
dc.subjectNeuronsen_GB
dc.subjectStability analysisen_GB
dc.subjectVisualizationen_GB
dc.subjectTime series analysisen_GB
dc.subjectJacobian matricesen_GB
dc.subjectTrajectoryen_GB
dc.subjectnonlinear time series analysisen_GB
dc.subjectDynamicsen_GB
dc.subjectecho-state network (ESN)en_GB
dc.subjectrecurrence plot (RP)en_GB
dc.subjectrecurrence quantification analysis (RQA)en_GB
dc.titleInvestigating Echo-State Networks Dynamics by Means of Recurrence Analysisen_GB
dc.typeArticleen_GB
dc.date.available2017-03-01T16:38:48Z
exeter.place-of-publicationUnited Statesen_GB
dc.descriptionThis is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.en_GB
dc.identifier.journalIEEE Transactions on Neural Networks and Learning Systemsen_GB


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