Epilepsy Detection in EEG Using Grassmann Discriminant Analysis Method

Epilepsy is marked by seizures stemming from abnormal electrical activity in the brain, causing involuntary movement or behavior. Many scientists have been working hard to explore the cause of epilepsy and seek the prevention and treatment. In the field of machine learning, epileptic diagnosis based on EEG signal has been a very hot research topic; many methods have been proposed, and considerable progress has been achieved. However, resorting the epileptic diagnosis techniques based on EEG to the reality applications still faces many challenges. Low signal-to-noise ratio (SNR) is one of the most important methodological challenges for EEG data collection and analysis. This paper discusses an automated diagnostic method for epileptic detection using a Fréchet Mean embedded in the Grassmann manifold analysis. Fréchet mean-based Grassmann discriminant analysis (FMGDA) algorithm to implement the EEG data dimensionality reduction and clustering task. The method is resorted to reduce Grassmann data from high-dimensional data to a relative lower-dimensional data and maximize between-class distance and minimize within-class distance simultaneously. Every EEG feature is mapped into the Grassmann manifold space first and then resort the Fréchet mean to represent the clustering center to carry out the clustering work. We designed a detailed experimental scheme to test the performance of our proposed algorithm; the test is assessed on several benchmark datasets. Experimental results have delivered that our approach leads to a significant improvement over state-of-the-art Grassmann manifold methods.

Mean and Variance of Phylogenetic Trees

We describe the use of the Fréchet mean and variance in the Billera–Holmes–Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, and, despite its stickiness property, is more likely to be binary than the majority-rule consensus tree. We show that the Fréchet variance is faster and more precise than commonly used variance measures. The Fréchet mean and variance are more theoretically justified, and more robust, than previous estimates of this type and can be estimated reasonably efficiently, providing a foundation for building more advanced statistical methods and leading to applications such as mean hypothesis testing and outlier detection.