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When nonlinear measures are estimated from sampled temporal signals withfinite-length, a radius parameter must be carefully selected to avoid a poorestimation. These measures are generally derived from the correlation integralwhich quantifies the probability of finding neighbors, i.e. pair of pointsspaced by less than the radius parameter. While each nonlinear measure comeswith several specific empirical rules to select a radius value, we provide asystematic selection method. We show that the optimal radius for nonlinearmeasures can be approximated by the optimal bandwidth of a Kernel DensityEstimator (KDE) related to the correlation sum. The KDE framework providesnon-parametric tools to approximate a density function from finite samples(e.g. histograms) and optimal methods to select a smoothing parameter, thebandwidth (e.g. bin width in histograms). We use results from KDE to derive aclosed-form expression for the optimal radius. The latter is used to computethe correlation dimension and to construct recurrence plots yielding anestimate of Kolmogorov-Sinai entropy. We assess our method through numericalexperiments on signals generated by nonlinear systems and experimentalelectroencephalographic time series.

Radius selection using kernel density estimation for the computation of nonlinear measures