Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.When a nonlinear dynamical system is externally modulated by an information-carrying signal, its erratic response hides an intricate property: Consistency. It is difficult to estimate from time series whether or not the variability in the output is entirely determined by the driving signal. For autonomous chaotic systems it is well-known that their inherent instability gives rise to a certain level of unpredictability. For a driven system, this means that a part of the variability of its output does not depend on the drive. Consistency quantifies the degree of this dependency through a replica test. The nonlinear system is repeatedly driven by the same signal, and the corresponding responses are compared. We apply this concept to echo-state networks, a class of artificial neural networks with a fixed random internal connectivity. Such networks have been successfully utilized for sequential processing tasks like nonlinear time series prediction and spoken digit recognition. Studying the consistency property allows for a more comprehensive understanding of the dynamical response and for tailoring the network systematically towards enhanced functionality and a wider range of applications.
Online music databases have increased signicantly as a consequence of the rapid growth of the Internet and digital audio, requiring the development of faster and more efficient tools for music content analysis. Musical genres are widely used to organize music collections. In this paper, the problem of automatic music genre classification is addressed by exploring rhythm-based features obtained from a respective complex network representation. A Markov model is build in order to analyse the temporal sequence of rhythmic notation events. Feature analysis is performed by using two multivariate statistical approaches: principal component analysis (unsupervised) and linear discriminant analysis (supervised). Similarly, two classifiers are applied in order to identify the category of rhythms: parametric Bayesian classifier under gaussian hypothesis (supervised), and agglomerative hierarchical clustering (unsupervised). Qualitative results obtained by Kappa coefficient and the obtained clusters corroborated the effectiveness of the proposed method. arXiv:0911.3842v1 [physics.data-an]
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