Phase space reconstruction, geometric filtering based Fisher discriminant analysis and minimum distance to the Riemannian means algorithm for epileptic seizure classification

•The PSR approach is employed to construct the covariance matrices.•It is used as the feature descriptor for characterizing the chaotic states of EEGs.•The geodesic filter with the Fisher discriminant analysis algorithm is employed.•It is used to enhance the class related information in the vector space.•The minimum distance to the Riemannian means classifier is applied. Most clinicians observe the changes of the electroencephalograms (EEGs) via the visual inspection of the recorded signals of the patients. However, the visual inspection is time consuming. Also, it is subjective and empirical. Therefore, designing an accurate and an automatic epilepsy classification system has a profound significance for reducing the workload of the medical officers. First, this paper applies the phase space reconstruction (PSR) method for constructing the covariance matrix for characterizing the chaotic states of the EEGs. The covariance matrices are symmetric positive definite (SPD) matrices used as the feature descriptors of the EEGs. This set of the covariance matrices is in fact a kind of the Riemannian manifold. Denote this Riemannian manifold as M. Secondly, the tangent space at the Riemannian geometric mean is computed via the logarithmic mapping operator. Denote this tangent space as TM. This tangent space TM is a kind of the Euclidean space containing a point in the Riemannian manifold M. That is, the SPD matrices in the Riemannian manifold M are mapped to the matrices in the tangent space TM at the Riemannian geometric mean via the logarithmic mapping operator. Then, these matrices in the tangent space TM are further mapped to the tangent feature vectors. The set of the tangent feature vectors is a kind of the vector space. Denote this vector space as VT. Thirdly, the transformation matrix based on the Fisher discrimination analysis (FDA) is used to map the high dimensional vectors in the vector space VT to the low dimensional vectors in another vector space. Then, the discriminative vectors are projected back to the Riemannian manifold M via the exponential mapping operator. Finally, the minimum distance to the Riemannian means (MDRM) algorithm is applied for performing the epileptic seizure classification. The computer numerical simulations are conducted based on three well known EEGs epileptic seizure datasets. Overall, our proposed method achieves the best performances for three datasets compared to the state of the art methods. Also, the computational compl