# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
## 3 Results
### Brain Signal Classification
#### 3.1.2 Efficient Data Augmentation for BCI  
Small datasets are common in many EEG applications. This is especially the case when developing systems for automatically detect some brain disease or brain injuries. Basically, because sometimes it is not easy or just impossible to have enough patients from which to record EEG or iEEG signals. MI-BCI systems for neurorehabilitation require a calibration step before being used. This is due to the fact that the system needs a classifier which is particular for each subject and session because, for example, the location of the electrodes in each session will never be exactly the same. The Common Spatial Pattern (CSP) algorithm [63] is habitually used to extract features. This calibration step implies recording several MI frames which will be used to extract the CSP filters and train the classifier. Each frame is composed by the EEG recordings of a particular trial. Since the quality of the classifier can be greatly improved by using a large number of frames from each type of MI [63], it is habitual to record 100 or more frames, in total. Taking into account that the MI paradigm can last about 10 s per frame, approximately a minimum of 16 min will be employed in the recording session. Over that, the time needed to set up the EEG montage has to be added. A way to shorten the calibration time is by reducing the number of registered frames but generating artificial ones to keep high the total number of frames. While available data augmentation techniques are proved to be efficient to boost the training of neural networks and support vector machines, they where developed mainly for image datasets, where natural transformations are coping and rotations, for example. These type of transforms have no sense for EEG data and new methods for data augmentation need to be developed. Methods based on signal decomposition and recombination of its main components are a natural way to solve that issue. In [52], the authors developed, for the first time, a method to generate artificial frames based on an EMD decomposition/combination strategy. Starting from a real frame collection, a new artificial frame of a specific class is built as described in Figure 3, comprising the following steps:  
1. Randomly select \(N\) frames from the set of frames belonging to the selected class. 2. Decompose, using EMD, each one of the \(N\) frames, generating a set of IMFs per channel and frame. Then, select the first IMF from the first selected frame (one per channel and keeping the same position for each channel), the second IMF from the second selected frame, and successively until the \(N\)th frame, which contributes with its \(N\)th IMF. 4. Add up all the IMFs corresponding to the same channel to build each new EEG channel of the new artificial frame. Using this method, authors in [52] were able to diminish the amount of acquired data for the calibration step in a BCI scenario while maintaining the performance. Specifically, they replaced original frames with artificial frames and tested the behaviour of the classifier derived from the data. Depending on the percentage of artificial frames in the data, they concluded that up to 50% of the original frames could be replaced without affecting the classifier's performance as it is presented in Table 2. The performance of each classifier was validated trough the median absolute deviation (MAD) method to detect outliers [64], and the dispersion ratio \(R\) was calculated as  
\[R=|(x-\tilde{x})/MAD|, \tag{8}\]  
where, for a set of measures, \(\tilde{x}\) is the median value and \(x\) is the measure to be tested. In the experiments, the error rate of the classifier was tested. Usually, if \(R<3\) the measure \(x\) is not considered to be an outlier, i.e., this classifier had a similar behaviour even if a specific percentage of real frames was replaced by artificial frames.