Narrow Results

To identify precursors of epileptic seizures, an EEG characteristic analysis is carried out based on a roughness-length method, where fractal dimensions and intercept values are extracted to measure the structure complexity and the amplitude roughness of EEG signals in different phases. Using the significant changes of the fractal dimension and intercept in the preictal phase with respect to those in the interictal phase, a patient-specific seizure prediction algorithm is then proposed by combining with a gradient boosting classifier. The probabilistic outputs of the trained gradient boosting classifier are further processed by threshold comparison and rule-based judgment to distinguish preictal EEG from interictal EEG and to generate seizure alerts. The prediction algorithm was evaluated on 20 patients’ intracranial EEG recordings from the Freiburg EEG database, which contains the preictal periods of 65 seizures and 499h interictal EEG. Setting the seizure prediction horizon as 2min, averaged sensitivity values of 90.42% and 91.67% with averaged false prediction rates of 0.12/h and 0.10/h were achieved for seizure occurrence periods of 30 and 50min, respectively. These results demonstrate the ability of fractal dimension and intercept metrics in predicting the occurrence of seizures.

The following sections are included:

• INTRODUCTION

• POPULATION PARAMETERS AND THE REGRESSION MODELS
  • Data Description
  • Building the Population Regression Model
  • Sample Versus Population Regression Model

• THE LEAST-SQUARES ESTIMATION OF α AND β
  • Scatter Diagram
  • The Method of Least Squares
  • Estimation of Intercept and Slope

• STANDARD ASSUMPTIONS FOR LINEAR REGRESSION

• THE STANDARD ERROR OF ESTIMATE AND THE COEFFICIENT OF DETERMINATION
  • Variance Decomposition
  • Standard Error of Residuals (Estimate)
  • The Coefficient of Determination

• THE BIVARIATE NORMAL DISTRIBUTION AND CORRELATION ANALYSIS
  • The Sample Correlation Coefficient
  • The Relationship Between r and b
  • The Relationship Between r and R²

• Summary

• Appendix 13A Derivation of Normal Equations and Optimal Portfolio Weights

• Appendix 13B The Derivation of Equation 13.16

• Appendix 13C The Bivariate Normal Density Function
  • Using a Mathematics Aptitude Test to Predict Grade in Statistics

• Appendix 13D American Call Option and the Bivariate Normal CDF
  • Valuating American Option

• Questions and Problems