# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
## 3 Results
### Brain Signal Classification
#### 3.1.3 Epileptic Focal Detection with Limited Data  
Epilepsy is a general term for a condition that causes repetitive seizures caused by excessive activity of neurons in the cerebrum, and such excessive activity is detected on EEG tests. Focal epilepsy, in which a part of the brain becomes abnormally excited and causes seizures, may be reduced or cured by removing the abnormally excited part of the brain (epileptogenic zone). Identification of the epileptogenic area requires intracranial electroencephalography (iEEG), in which electrodes are placed intracranially and measured, as well as brain imaging evaluation such as MRI. The identification of the epileptogenic zone requires a long-term iEEG recording. Besides, the number of clinical experts (epileptologist) is limited. Therefore, the automated identification of the brain area of seizure onset of focal epilepsy (a.k.a automated focal identification) using interictal (non-seizure) iEEG signals is in strong demand. However, clinical iEEG data usually stay in each medical facility and cannot be in public, so that the amount of data available for training a machine learning model is also limited. This situation brings the necessity of appropriate processing for a small dataset. A possible and straightforward way to cope with this problem is data augmentation. Two types of approaches to the iEEG data augmentation have been proposed recently. The first method is to augment data in the signal domain [54]. The second method is the data augmentation in the feature domain [56]. Both methods work efficiently in identifying focal locations from interictal iEEG. The data augmentation in the signal domain applies orthogonal transforms such as the discrete Fourier transform, the discrete cosine transform (DCT), and the discrete wavelet transform (DFT) to the raw iEEG signal, and then the transform coefficients are shuffled across multiple epochs (or segments). [PERSON] et al. constructed an efficient and sophisticated method for the data augmentation based on the DCT [54] and applied to the Bern-Barcelona dataset [65], which is a well-known dataset  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & **S01** & **S02** & **S03** & **S04** & **S05** & **S06** & **S07** \\ \hline
**AF(\%)** & **R  
consisting of epileptictiEEG signal at focal and non-focal locations. The steps to increase the number of samples are summarized as follows:  
1. Randomly choose seven iEEG signals from the dataset and apply the DCT to obtain the spectrum. 2. Segment the spectrum into the seven physiological frequency bands (Delta: 0-4 Hz, Theta: 4-8 Hz, Alpha: 8-13 Hz, Beta: 13-30 Hz, Gamma: 30-80 Hz, Ripple: 80-150 Hz, and Fast Ripple: 150-Nyquist Hz), extract one frequency band of each of the decompositions, from lowest to highest frequencies, and merge the seven extracted components (frequency bands) to create a new artificial spectrum. For example, we can extract the delta, the theta, the alpha, the gamma, the ripple, and the fast ripple from the first, the second, the third, the fourth, the fifth, the sixth, and the seventh signal, respectively. 3. Apply the inverse DCT to the artificial spectrum in the frequency domain to obtain an artificial signal in the time-domain. This is illustrated in Figure 4. The above procedure should be applied to focal and non-focal signals separately. Since this approach to the data augmentation increases the number of samples in the signal-domain, it may be suitable for deep learning-based techniques. In the work [54], the authors successfully applied this data augmentation for a convolutional neural network to identify the focal signals. The data augmentation strategy demonstrated to be useful: using 20% of available real data plus artificial data, the classifier was able to improve its accuracy results to 83.91%, compared to 81.52% obtained using only real data. The other approach to data augmentation is a method in the feature-domain.