ABSTRACT
In many practical classification problems it is important to distinguish false positive from false negative results when evaluating the performance of the classifier. This is of particular importance for medical diagnostic tests. In this context, receiver operating characteristic (ROC) curves have become a standard tool. Here we apply this concept to characterize the performance of a simple neural network. Investigating the binary classification of a perceptron we calculate analytically the shape of the corresponding ROC curves. The influence of the size of the training set and the prevalence of the quality considered are studied by means of a statistical-mechanics analysis.
Subject(s)
Neural Networks, Computer , ROC Curve , Biophysical Phenomena , Biophysics , False Negative Reactions , False Positive Reactions , Humans , Learning , Models, Statistical , Sample SizeABSTRACT
We present a systematic approach for detecting nonlinear components in heart rate variability (HRV). The analysis is based on twenty-three 48-h Holter recordings in healthy persons during sinus rhythm. Although many segments of 1,024 R-R intervals are stationary, only few stationary segments of 8,192-32,768 R-R intervals can be found using a test of Isliker and Kurths (Int. J. Bifurcation Chaos 3:1573-1579, 1993.). By comparing the correlation integrals from these segments and corresponding surrogate data sets, we reject the null hypothesis that these time series are realization of linear processes. On the basis of a test statistic exploring the differences of consecutive R-R intervals, we reject the hypothesis that the R-R intervals represent a static transformation of a linear process using optimized surrogate data. Furthermore, time irreversibility of the heartbeat data is demonstrated. We interpret these results as a strong evidence for nonlinear components in HRV. Thus R-R intervals from healthy persons contain more information than can be extracted by linear analysis in the time and frequency domain.
