@article {18533,
	title = {Determination of the Edge of Criticality in Echo State Networks Through Fisher Information Maximization},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {29},
	year = {2018},
	month = {March},
	pages = {706-717},
	keywords = {Echo state network (ESN), echo state networks, edge of criticality, ESN, Fisher information, Fisher information matrix, Fisher information maximization, Jacobian matrices, Learning systems, Neurons, nonparametric estimation, nonparametric estimator, nonparametric statistics, prediction error, Probability density function, recurrent neural nets, recurrent neural networks, Reservoirs, RNN, short-term memory capacity, Training},
	issn = {2162-237X},
	doi = {10.1109/TNNLS.2016.2644268},
	author = {Livi, Lorenzo and Bianchi, Filippo Maria and Alippi, Cesare}
}
@article {18508,
	title = {Investigating echo state networks dynamics by means of recurrence analysis},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {29},
	year = {2018},
	month = {02/2018},
	pages = { 427 - 439},
	abstract = {In this paper, we elaborate over the well-known
interpretability issue in echo state networks. The idea is to investigate
the dynamics of reservoir neurons with time-series analysis
techniques taken from research on complex systems. 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 two-dimensional representation offered by RPs
provides a way for visualizing the high-dimensional dynamics of
a reservoir. Our results suggest that, if the network is stable,
reservoir and input denote similar line patterns in the respective
RPs. Conversely, the more unstable the ESN, the more the RP
of the reservoir presents instability patterns. As a second result,
we show that the Lmax measure is highly correlated with the
well-established maximal local Lyapunov exponent. This suggests
that complexity measures based on RP diagonal lines distribution
provide a valuable tool to quantify the degree of 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 verify
that the determination of the edge of stability provided by such
RQA measures is more accurate than two well-known criteria
based on the Jacobian matrix of the reservoir. Therefore, we
claim that RPs and RQA-based analyses can be used as valuable
tools to design an effective network given a specific problem.},
	doi = {10.1109/TNNLS.2016.2630802},
	author = {Bianchi, Filippo Maria and Livi, Lorenzo and Alippi, Cesare}
}
@conference {18530,
	title = {Time series kernel similarities for predicting Paroxysmal Atrial Fibrillation from ECGs},
	booktitle = { IJCNN 2018 : International Joint Conference on Neural Networks},
	year = {2018},
	month = {07/2018},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Rio, Brazil},
	author = {Bianchi, Filippo Maria and Livi, Lorenzo and Ferrante, Alberto and Milosevic, Jelena and Malek, Miroslaw}
}
@conference {18538,
	title = {Critical echo state network dynamics by means of Fisher information maximization},
	booktitle = {2017 International Joint Conference on Neural Networks (IJCNN)},
	year = {2017},
	month = {May},
	keywords = {Asymptotic stability, critical phase transitions, echo state network, edge of criticality, Electronic mail, ESN, Estimation, estimation theory, FIM, Fisher information matrix, Fisher information maximization, hidden neurons activations, high short term memory capacity, input signal, low prediction error, network dynamics, network theory (graphs), Neurons, optimisation, Probability density function, recurrent neural nets, Reservoirs, signal processing, statistics, Tuning, unsupervised approach, unsupervised learning},
	doi = {10.1109/IJCNN.2017.7965941},
	author = {Bianchi, Filippo Maria and Livi, Lorenzo and Jenssen, Robert and Alippi, Cesare}
}
@article {18532,
	title = {Multiplex visibility graphs to investigate recurrent neural network dynamics},
	journal = {Nature-Scientific reports},
	volume = {7},
	year = {2017},
	month = {03/2017},
	pages = {44037-44049},
	chapter = {44037},
	doi = {doi:10.1038/srep44037},
	author = {Bianchi, Filippo Maria and Livi, Lorenzo and Alippi, Cesare and Jenssen, Robert}
}
