^{1}

^{1}

^{*}

Characterized by recurrent and rapid seizures, epilepsy is a great threat to the livelihood of the human beings. Abnormal transient behaviour of neurons in the cortical regions of the brain leads to a seizure which characterizes epilepsy. The physical and mental activities of the patient are totally dampened with this epileptic seizure. A significant clinical tool for the study, analysis and diagnosis of the epilepsy is electroencephalogram (EEG). To detect such seizures, EEG signals aids greatly to the clinical experts and it is used as an important tool for the analysis of brain disorders, especially epilepsy. In this paper, the high dimensional EEG data are reduced to a low dimension by incorporating techniques such as Fuzzy Mutual Information (FMI), Independent Component Analysis (ICA), Linear Graph Embedding (LGE), Linear Discriminant Analysis (LDA) and Variational Bayesian Matrix Factorization (VBMF). After employing them as dimensionality reduction techniques, the Neural Networks (NN) such as Cascaded Feed Forward Neural Network (CFFNN), Time Delay Neural Network (TDNN) and Generalized Regression Neural Network (GRNN) are used as Post Classifiers for the Classification of Epilepsy Risk Levels from EEG signals. The bench mark parameters used here are Performance Index (PI), Quality Values (QV), Time Delay, Accuracy, Specificity and Sensitivity.

For a majority of the biomedical scientists, medical practitioners and biomedical engineers, a lot of research is in progress about the functioning of the human brain [

When performing the analysis of any particular information, high dimensional data are found often in most of the disciplines. The dimensions of the data must be made low and it should be regularized because only then approximation techniques can be applied easily [

EEG signal processing has several vital constraints. In EEG signal processing, a huge number of signals have to be processed, which is generally very difficult since all the signals are highly interdependent. Each signal is very unique in an EEG and hence it is not repeatable. Also, based on the characteristics of the equipment or source, EEG signals are often noisy [

For the performance assessment of the epilepsy risk levels using the FMI, ICA, LGE, LDA and VBMF as Dimensionality Reduction technique followed by NN as Post Classifiers, the raw EEG data of 20 epileptic patients who were under treatment in the Neurology Department of Sri Ramakrishna Hospital, Coimbatore in European Data Format (EDF) are taken for study. The EEG is recorded by placing electrodes on the scalp according to the International 10 - 20 system. Sixteen channels of EEG are recorded simultaneously for both referential montages, where all electrodes are referenced to a common potential like ear, and bipolar montages, where each electrode is referenced to an adjacent electrode. Recordings are made while the patient is fully awake but in resting condition and include periods of eyes open, eyes closed, hyperventilation and photonic stimulation. Amplification is provided by an EEG-machine (Siemens Minograph Universal). Before placing the electrodes, the scalp is cleaned, lightly abraded and electrode paste is applied between the electrode and the skin. By means of this application of electrode paste, the contact impedance is less than 10 kW. Generally disk like surface electrodes are used. In some cases, needle electrodes are used to pick up the EEG signals. The signals are recorded with the speed of 30 mm/s.

The pre processing stage of the EEG signals is given more attention because it is vital to use the best available technique in literature to extract all the useful information embedded in the non-stationary biomedical signals [

The dimensions of the EEG data are stored by a pre-processing step known as Dimensionality Reduction (DR). By separating a set of important features that goes hand in hand with certain important criteria, the dimensions of the data can be reduced. The impact of the reduced dimensions has a vital effect to play in the classification process. Each epoch contains 400 values and hence the total volume for a patient is around 25,600 samples. So it absolutely necessary to reduce the dimensions of the data for smooth processing of the EEG signals. In a high-dimensional data set, it is important to understand that not all the obtained variables by appropriate measurements are utilized for analyzing the underlying area of interest.

Assuming that there are totally “n” linear mixtures as

The vector-matrix notation is utilized completely and the above equation can be written as follows [

where A denotes the matrix with particular elements

importance of columns of matrix A, the model can be written as follows

columns of matrix A. It is considered as a generative model where an observed data is described clearly. If the matrix A is estimated, then the computation of its inverse, say P, is obtained easily and then the independent component is obtained as follows

This process generally involves Graph Embedding, Linearization and Kernelization procedures but for

dimensionality reduction of EEG signals the following procedure is considered. A sample set for model training is represented as a matrix

This main function always transforms

Therefore it is mathematically represented as follows

It is a filter method where the irrelevant features can be easily reduced. Enrichment of the mutual information is done using the fuzzy concept [

The entropy of class C is then calculated as follows

The normalized Fuzzy entropy measure is then calculated as follows

It is a popular technique for dimensionality reduction [

To determine the LDA explicitly, it is vital to consider a multiclass pattern recognition and classification problem with e classes. Let

It refers to a method for uncovering a very low-rank structure of a particular data [

The over fitting problem is successfully alleviated by the Bayesian treatment of matrix factorization.

Several post classifiers for the classification of epilepsy risk levels was considered in [

To understand the cascaded feed forward neural network, feed forward back propagation model is considered. The feed forward back propagation model consists of input, hidden and output layers. The learning algorithm used here is Back Propagation Networks (BPN). During the training phase, from the input layer of the network to the output layer of network, calculations were carried out and the generated error values are then forwarded to the prior layers [

where

This network does not require a training procedure which is iterative in nature. It is always very consistent in its attributes. For the estimation of the continuous variables, GRNN can be used easily. The approximation of arbitrary function between input and output vectors are done quite easily in this model [

It is an Artificial Neural architecture, where the main intention of it is to work on data which is sequential in manner and it is feed forward in nature. The TDNN units easily recognize the features which are highly independent of time shift [

The Levenberg-Marquardt (LM) algorithm is the basic training method for minimization of MSE (Mean Square Error) criteria, due to its fast converging properties and robustness [

where W(k) is the weight at the k^{th} iteration, α is the learning rate, (k) is the difference between NN output and the expected output. DW(k) is the weighted difference between the k^{th} and (k − 1)^{th} iteration (this item is optimal), and m is the momentum constant. In some adaptive algorithms, α change with time, but this requires many iterations and leads to a high computational burden. Fortunately, the non-linear least squares Gauss-Newton has been used to solve many supervised NN training problem.

For FMI, ICA, LGE, LDA and VBMF as dimensionality reduction techniques and Neural Networks as Post Classifiers, based on the Performance Index, Quality values, Time Delay and Accuracy the simulated result values are plotted in Tables 1-3 respectively. The formulae for the Performance Index (PI), Sensitivity, Specificity and Accuracy are given as follows

where PC―Perfect Classification, MC―Missed Classification, FA―False Alarm.

The Sensitivity, Specificity and Accuracy measures are stated by the following

PC | MC | FA | PI | Sensitivity | Specificity | Time | Quality | Accuracy | |
---|---|---|---|---|---|---|---|---|---|

FMI + GR-NN | 100 | 0 | 0 | 100 | 100 | 100 | 2 | 25 | 100 |

ICA + GR-NN | 100 | 0 | 0 | 100 | 100 | 100 | 2 | 25 | 100 |

LDA + GR-NN | 100 | 0 | 0 | 100 | 100 | 100 | 2 | 25 | 100 |

LGE + GR-NN | 93.19 | 0.83 | 5.97 | 92.38 | 94.02 | 99.16 | 1.91 | 20.79 | 96.59 |

VBMF + GR-NN | 100 | 0 | 0 | 100 | 100 | 100 | 2 | 25 | 100 |

PC | MC | FA | PI | Sensitivity | Specificity | Time | Quality | Accuracy | |
---|---|---|---|---|---|---|---|---|---|

FMI + TD-NN | 100 | 0 | 0 | 100 | 100 | 100 | 2 | 25 | 100 |

ICA + TD-NN | 95.27 | 2.22 | 2.5 | 94.52 | 97.5 | 97.77 | 2.03 | 22.42 | 97.63 |

LDA + TD-NN | 95.06 | 0.69 | 4.23 | 94.51 | 95.76 | 99.30 | 1.94 | 21.90 | 97.53 |

LGE + TD-NN | 96.45 | 0 | 3.54 | 96.10 | 96.45 | 100 | 1.92 | 22.55 | 98.22 |

VBMF + TD-NN | 94.79 | 0.34 | 4.86 | 94.19 | 95.13 | 99.65 | 1.91 | 21.66 | 97.39 |

PC | MC | FA | PI | Sensitivity | Specificity | Time | Quality | Accuracy | |
---|---|---|---|---|---|---|---|---|---|

FMI + CFF-NN | 93.26 | 1.45 | 5.30 | 92.41 | 94.72 | 98.54 | 1.95 | 21.00 | 96.63 |

ICA + CFF-NN | 92.26 | 1.87 | 5.86 | 90.91 | 94.13 | 98.12 | 1.95 | 20.78 | 96.13 |

LDA + CFF-NN | 94.30 | 1.73 | 3.95 | 93.72 | 96.04 | 98.26 | 1.99 | 21.65 | 97.15 |

LGE + CFF-NN | 93.81 | 0.57 | 5.62 | 92.95 | 94.37 | 99.44 | 1.90 | 21.15 | 96.90 |

VBMF + CFF-NN | 93.26 | 0.62 | 6.11 | 92.49 | 93.88 | 99.37 | 1.90 | 20.74 | 96.63 |

The Time Delay and the Quality Value Measures are given by the following

On the careful examination of

Thus the most used technique to capture the brain signals is the EEG signals. EEG always provides an excellent temporal resolution. EEG is considered as a highly complex human brain signal which consists of valid information about the functions of the brain and the other neurological disorders. EEG also plays a vital role for diagnosis of epilepsy, early detection of brain tumour, early detection of problems related to sleep etc. Epilepsy generally affects people from all ages but young infants and the elderly people are more prone to it. Epilepsy occurs due to abnormalities in the genetic mechanisms of humans or it may be due to developmental anomalies and infections in the central nervous system. It is quite difficult to extract the feature rhythms because the EEG signal is quite complex, stochastic and non-stationary in nature. Due to the abrupt and unpredictable nature of the epileptic seizures, the everyday routine life of an epileptic patient is severely affected. Since epilepsy is witnessed by sudden disturbances of the mental functions which results due to the excessive discharging of groups of cells in the brain, the epileptic EEG obtained from the scalp is characterized by synchronized periodic waveforms which have very high amplitude. Spikes and sharp waves too are found in between the seizures and hence the detection of it by an encephalographer is quite difficult as it requires skilled technicians who are in great demand nowadays. This leads to a prolonged diagnosis time period and also the expenditures related to it are too much to bear. Surgery may not be suitable to all the patients because it demands the consideration of other health risks also. Therefore, the seizures have to be detected in an automatic manner and it forms an integral part of biomedical research. This

research on epilepsy has therefore become an active interdisciplinary field of biomedical research. Thus the dimensions of the EEG signals were reduced using five different dimensionality reduction techniques and then it was classified by using three different types of Neural Network Post Classifiers. Results showed that FMI-GRNN, ICA-GRNN, LDA-GRNN, VBMF-GRNN and FMI-TDNN showed an accuracy of 100% with the highest quality

values as of 25. Future works plan to incorporate other neural networks and genetic algorithms for the epilepsy classification from EEG signals.

Harikumar Rajaguru,Sunil Kumar Prabhakar, (2016) A Unique Approach to Epilepsy Classification from EEG Signals Using Dimensionality Reduction and Neural Networks. Circuits and Systems,07,1455-1464. doi: 10.4236/cs.2016.78127