Understanding Epilepsy Seizure Structure Using Tensor Analysis
We introduce mathematical models based on multi-modal data construction and analysis approaches with a goal of understanding epilepsy seizure dynamics and developing automated and objective approaches for the analysis of large amounts of scalp electroencephalogram(EEG) data. We address two important problems in epilepsy diagnosis and treatment: seizure localization and seizure recognition.
We address the problem of identification of a seizure origin through an analysis of ictal EEG, which is proven to be an effective standard in epileptic focus localization. We rearrange multi-channel ictal EEG data as a third-order tensor with modes: time samples, scales and channels, through continuous wavelet transform(CWT).
Then we demonstrate that multiway analysis techniques, in particular Parallel Factor Analysis (Harshman 1970), can successfully model the complex structure of an epilepsy seizure, localize an epileptic seizure origin and extract artifacts. Furthermore, we introduce an approach for removing artifacts using multilinear subspace analysis (Acar et al. 2007).
In the figure above, we demonstrate the modeling of an epilepsy tensor by a 2-component PARAFAC model, where the first component corresponds to an eye-artifact while the second component represents a seizure. Top: Temporal (a1), spectral (b1) and spatial (c1) signatures of an eye-artifact. a1 represents the coefficients of time samples, b1 represents the coefficients of scales. Since there is a peak in higher scales on the plot of b1, it indicates that this artifact takes place at lower frequencies. c1 contains the coefficients of electrodes. These coefficients are demonstrated on a colormap using EEGLab (Delorme and Makeig 2004). Bottom: Temporal (a2), spectral (b2) and spatial (c2) signatures of a seizure. Similar to the first component, a2 represents the coefficients of time samples, b2 represents the coefficients of scales. There is a peak in lower scales on the figure corresponding to b2, which indicates that the seizure takes place at higher frequencies. Finally, c2 contains the coefficients of electrodes, which are used to localize the seizure around T4 and T6.
With a goal of differentiating between seizure and non-seizure (pre-seizure/post-seizure) periods, we extract various features from both time and frequency domains to represent scalp EEG recordings. We rearrange multi-channel EEG recordings as a third-order tensor with modes: time epochs, features and channels.
We then model the epilepsy feature tensor using a multilinear discriminant analysis based on Multilinear Partial Least Squares (N-PLS) (Bro 1996), which is the generalization of Partial Least Squares regression to tensors. This two-step approach facilitates the analysis of EEG data from multiple channels represented by several features from different domains. We build a supervised learning model, which is trained on some seizures of a patient and then tested on other seizures of that particular patient (patient-specific seizure recognition) or trained and tested on seizures of different patients (patient non-specific seizure recognition). We demonstrate that multi-modal data construction and analysis approach provides promising performance in terms of marking the seizure period automatically.