# A Study of EEG Feature Complexity in Epileptic Seizure Prediction
###### Abstract  
The purpose of this study is (1) to provide EEG feature complexity analysis in seizure prediction by inter-ictal and pre-ital data classification and, (2) to assess the between-subject variability of the considered features. In the past several decades, there has been a sustained interest in predicting epilepsy seizure using EEG data. Most methods classify features extracted from EEG, which they assume are characteristic of the presence of an epilepsy episode, for instance, by distinguishing a pre-ictal interval of data (which is in a given window just before the onset of a seizure) from inter-ictal (which is in preceding windows following the seizure). To evaluate the difficulty of this classification problem independently of the classification model, we investigate the complexity of an exhaustive list of 88 features using various complexity metrics, i.e., the Fisher discriminant ratio, the volume of overlap, and the individual feature efficiency. Complexity measurements on real and synthetic data testbeds reveal that that seizure prediction by pre-ictal/inter-ictal feature distinction is a problem of significant complexity. It shows that several features are clearly useful, without decidedly identifying an optimal set. data complexity measures; epileptic seizure; pre-ictal period; hand-engineered features; epilepsy prediction +
Footnote †: journal: Medical  
to drive a particular classifier. The performance of the classifier-and-features combination is then evaluated on some pertinent test data. The purpose of the evaluation is not to study the discriminant potency of the features independently of the classifier, although such a study is essential to inform on the features complexity, i.e., the features classifier-independent discriminant potency. In contrast, our study is concerned explicitly with classifier-independent relative effectiveness of features. The purpose is to provide a feature complexity analysis in seizure prediction by inter-ictal/pre-ital data classification, which evaluates features using classifier-independent and statistically validated complexity metrics, such as Fisher discriminant ratio and class overlap volume, to gain some understanding of the features relative potency to inform on the complexity of epilepsy seizure prediction and the level of classification performance one can expect. This can also inform on between-patients data variability and its potential impact on epileptic seizure prediction as a pattern classifier problem. Before presenting this analysis in detail, we briefly review methods that have addressed EEG feature-based epileptic seizure prediction. The statistical study in Reference [6] compared 30 features in terms of their ability to distinguish between the pre-ictal and pre-seizure periods, concluding that only a few features of synchronization showed discriminant potency. The method had the merit of not basing its analysis on a particular classifier. Rather, it measured a feature in pre-ictal and inter-ictal segments and evaluated the difference by statistical indicators, such as the ROC curve. This difference is subsequently mapped onto the ability of the feature to separate pre-ictal from inter-ictal segments. In general, however, epilepsy seizure prediction methods, such as Reference [7, 8], are classifier-based because they measure a feature classification potency by its performance using a particular classification algorithm. Although a justification to use the algorithm is generally given, albeit informally, feature potency interpretation can change if a different classifier is used. Observed feature interpretation discrepancies can often be explained by the absence of statistical validation in classifier-dependent methods. The importance of statistical validation has been emphasized in Reference [9], which used recordings of 278 patients to investigate the performance of a subject-specific classifier learned using 22 features.