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Computational Properties of Delay-Coupled Systems
|Advisor:||Mirasso, Claudio R.|
|Publisher:||CSIC-UIB - Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)|
Universidad de las Islas Baleares
|Abstract:||In this research work we study the computational properties of delay-coupled
systems. In particular, we use a machine learning technique known as
computing. In machine learning, a computer
to solve different tasks using
examples and without knowing explicitly their solution.
For the study of the computational properties, a numerical toolbox, written
in Python, was developed. This toolbox allows a fast implementation of the
different scenarios described in this thesis.
Using a reservoir computer, we studied several computational properties, focusing on its kernel quality, its ability to separate different input samples and
the intrinsic memory capacity. This intrinsic memory is related to the delayed-
feedback of the reservoir.
We used a delay-coupled system as reservoir to study its computational ability
in three different kinds of tasks: system’s modeling, time-series prediction and
The system’s modeling task was performed using the Nonlinear Autoregressive
Moving Average (of ten steps), NARMA10. The NARMA10 model creates autoregressive time series from a set of normally distributed random sequences.
The reservoir computer learns how to emulate the system using only the sequence of random numbers and the autoregressive time series, but without
knowing the equations of the NARMA10. The results of our approach are
equivalent to those published by other authors and show the computational
power of our method.
For the time-series prediction tasks, we used three kinds of time series: a model
that gives the variations in temperature of the sea surface that provoke El Niño
phenomenon, the Lorenz system and the dynamics of a chaotic laser. Different
scenarios were explored depending on the nature of the time series. For the
prediction of the variation in temperature of the sea surface, we perform estimations of one, three and six months in advance. The error was measured as the Normalized Root Mean Square Error (NRMSE). For the different prediction
horizons, we obtained errors of 2%, 8% and 24%, respectively.
The classification tasks were carried out for a Spoken Digit Recognition (SDR)
task and a real-world biomedical task. The SDR
was used to illustrate different scenarios of a machine learning problem. The biomedical task consists
on the automatic classification of heartbeats with cardiac arrhythmias. We use
the MIT-BIH Arrhythmia database, a widely used database in cardiology. For
comparison purposes, we followed the guidelines of the Association for the Advancement of Medical Instrumentation for the evaluation of arrhythmia-detector
algorithms. We used a biostatistical learning process named logistic regression
that allowed to compute the probability that a heartbeat belongs to a particular
This is in contrast to the commonly used linear regression. The results obtained in this work show the versatility and efficiency of our implemented reservoir computer. Our results are equivalent and show improvement over other reported results on this problem under similar conditions and using the same database. To enhance the computational ability of our delay-coupled system, we included a multivariate scheme that allows the consideration of different variables of a system. We evaluated the influence of this multivariate scenario using a time- series prediction and the classification of heartbeat tasks. The results show improvement in the performance of the reservoir computer in comparison with the same tasks in the univariate case.
|Description:||Tesis Doctoral presentada por Miguel Angel Escalona Morán para optar al título de Doctor, en el Programa de Física del Departamento de Física de la Universitat de les Illes Balears, realizada en el IFISC bajo la dirección de Claudio Mirasso, catedrático de universidad y Miguel Cornelles Soriano, contratado postdoctoral CAIB.|
|Appears in Collections:||(IFISC) Tesis|
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