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This section comprises a series of seizure prediction and feature reduction experiments, under the simplest experimental conditions, namely patient specific training, validation and test sets, single-channel feature-set and ictal datasets from the Freiburg EEG Database. The aim of this set of experiments is to evaluate the impact of reducing the feature-set on the learning performance, on a larger number of patients; in this case, all the patients from the Freiburg EEG Database. We aim to see whether general patterns, such as optimum number of features and highly ranked features, emerge among the population of tested patients. The outcome of this series of experiments is a set of feature rankings per Patient-File in addition to the performance measures of the respective learning models constructed at each dimensionality reduction step.

6.2.1 Methods For Single-Channel Dimensionality Reduction

In this section we present the data preparation and implementation steps undertook for conducting the stepwise dimensionality reduction experiment on single-channel Patient- Files from the Freiburg EEG Database.

Data Preparation of Single-Channel Data For Dimensionality Reduction

The data used in this experiment are from the Freiburg EEG Database. The unprocessed data are originally in ASCII format, comprising signal voltage recorded from 6 incoming channels at 256 Hz. Each patient has numerous ASCII files, which were organised based on the recorded segment and the incoming channel. These files were prepared according to steps described in chapter 4. The preparation steps resulted

in 21 Excel and Matlab Patient-Files, each of which contain 14 extracted features of three main categorisations: signal energy, wavelet transforms and non-linear dynamics. A list of the engineered features is presented in Table 6.1 for ease of reference.

Concept Features

Signal Energy

Accumulated energy Energy level

Energy variation (short term energy (STE)) Energy variation (long term energy (LTE))

Wavelet Transform Energy STE 1 (0Hz − 12.5Hz) Energy STE 2 (12.5Hz − 25Hz) Energy STE 3 (25Hz − 50Hz) Energy STE 4 (50Hz − 100Hz) Energy LTE 1 (0Hz − 12.5Hz) Energy LTE 2 (12.5Hz − 25Hz) Energy LTE 3 (25Hz − 50Hz) Energy LTE 4 (50Hz − 100Hz) Nonlinear system dynamics Correlation dimension Max Lyapunov Exponent

Table 6.1 Original 14 features extracted from EEG Channels – The feature-set is based on the work of Costa et al. (Costa et al. 2008).

The features were calculated using a moving window analysis for each 5-second block of data, all of which were labeled with the ictal state of the patient. The seizure-state labels take values of 1 - 4, which respectively represent inter-ictal, pre-ictal, ictal and post-ictal states of the brain. Each prepared file holds 1 hour of data per seizure, comprising all 4 classes. The Patient-Files contain 1 to 5 seizure recordings for each patient. The rendered 14 features were extracted from a single focal EEG channel for each patient. The 5 remaining channels were not used in this experiment.  

Implementation of Dimensionality Reduction on Single-Channel Data

This Dimensionality Reduction study is composed of a series of segregated experiments conducted on each individual Patient-File, as shown in Figure 6.1.

Each preprocessed Patient-File was separately normalised to values in the range [0, 1] for ReliefF feature selection algorithm, and was split into 70% training-set and 30% test-set, using a random seed permutation. The feature selection method, namely ReliefF, was implemented on each training-set for a total of 10 runs. The outcome of the total runs of each feature selection algorithm was an f ×10 matrix of rankings

where f is the total number of features, and each row is a ranking r=1…f , where r=1

accounts for the best feature and r= f accounts for the worst feature. Best and worst are determined based on the ranking criteria of ReliefF feature selection algorithm, as described in section 2.3. The rankings for each feature were averaged over 10 runs, and the features were sorted according to the ascending average rank. Table 6.2 lists an example of such rankings for Patient-File 2.

ReliefF Ranks Accumulated energy 1 Energy level 8 Energy STE 7 Energy LTE 4 Lyapunov exponents 2 Correlation dimension 9 Energy STE 1 10 Energy STE 2 5 Energy STE 3 3 Energy STE 4 6

Energy LTE level 1 11

Energy LTE level 2 14

Energy LTE level 3 13

Energy LTE level 4 12

Table 6.2 Rankings of the 14 features of Patient-File 2 ReliefF feature selection method – The features were based on (Costa et al. 2008) and were obtained from the default EEG channel for the patient.

Figure 6.1 the architecture of the Dimensionality Reduction Experiment – The system consists of a Pre-processing Module and a Learning Module. The data preparation and initial experimental setup takes place in the Pre-processing Module, which varies for each experiment. This is separated from the learning and classification task in the Learning Module, which remains unchanged for the main part of the experiments.  

For each Patient-File, the constructed ranking table was used to reduce the feature subset in a stepwise manner. For each ranking table of size f , n features were removed at each step, for s= f / 2 number of steps. In this particular experiment,

f =14 and s=7. The n features removed at each step were those with the lowest ranks. This resulted in d = f / 2 number of training-sets and test-sets. Each training-

file subset was separately fed into a learning module, where the training-set was further divided into random permutations of training-set (90%) and validation set (10%) over several folds for parameter selection purposes.

The Multi-class Support Vector Machine (See Chapter 2) was used in the learning module in order to learn mappings from training features, and use them to classify the blocks of test and validation data into inter-ictal (1), pre-ictal (2), ictal (3) and post-ictal (4) states.

The Multi-class SVM classifier was implemented using the LIBSVM software package for Matlab (Chang & Lin 2011; Csie.ntu.edu.tw 2013) , in which a ‘one- against-one’ approach (Knerr et al. 1990; Kreßel 1999) was used, where for each number of labels k (k-1)/2 classifiers are constructed. Error in learning was penalised (Chang & Lin 2011) based on weights specified for each class:

  ₍₁₎

The learning algorithm penalises the misclassification of each label in accordance with the corresponding weight W, where  is the weight for inter-ictal misclassification;  is for pre-ictal,  for ictal and  for post-ictal misclassification. Using misclassification weights is especially useful when working with unbalanced datasets, where the occurrence of a certain class is more probable than the others. By carefully choosing the weights, misclassification errors can be avoided. In our dataset, class 1, the inter-ictal class, had a higher frequency than the other 3 classes. For each hour of ictal data, there were approximately 5 minutes of seizure data, 5 minutes of pre-ictal and 5-minutes of post-ictal data, yielding a highly imbalanced dataset where ~75% of the dataset (45 minutes per 1 hour of ictal data) consisted of inter-ictal data with little detectible neuronal abnormality. We therefore set  to 1 and set all the other weights

as ,  in an effort to avoid inaccurate classification and

performance outcomes.

k

W1 = 1

W2 = int_ictal/pre_ictal

W3 = int_ictal/ictal W4 = int_ictal/post_ictal

W₁

W2 W3 W4

W1