IEEE Second International Conference on Data Stream Mining & Processing August 21-25, 2018, Lviv, Ukraine 978-1-5386-2874-4/18/$31.00 ©2018 IEEE 392 Analysis of EEG using Multilayer Neural Network with Multi-Valued Neurons Igor Aizenberg Manhattan College Riverdale New York, USA igor.aizenberg@manhattan.edu Zain Khaliq Manhattan College Riverdale New York, USA zkhaliq01@manhattan.edu Abstract—There is a wealth of analysis techniques that can be used in analyzing data of such a nature as EEG (Electroencephalogram), yet there are still many more ways and possibilities of analysis techniques to consider in order to produce a method that far exceeds the capabilities of the prevalent method. Since a multilayer neural network with multi-valued neurons (MLMVN) was successfully used earlier to decode EEG signals in a brain/computer interface (BCI) by analysis of their Fourier transform, it seemed very attractive to use it as a tool for EEG analysis. This work aims to further investigate how a complex-valued machine learning tool can be used to analyze EEG in the frequency domain. Our goal was to check how Fourier transform and complex wavelet transform of EEG can be analyzed using MLMVN in order to diagnose epilepsy, its remission or absence. We worked with a commonly used benchmark data set of epilepsy-related EEGs. The analysis of the transformed data was performed to determine a set of relevant statistical characteristics of DTCWT and Fourier transform components, which were then used as inputs of the MLMVN. The obtained results show a very high efficiency of the proposed approach. Keywords—Complex-Valued Neural Networks, Multi-Valued Neuron, Multilayer Neural Network with Multi-Valued Neurons, MLMVN, EEG, Fourier transform I. INTRODUCTION We would like to use here MLMVN to analyze EEG in the frequency domain. MLMVN is a representative of complex-valued neural networks (CVNN) family. There is plenty of work done that states the use of CVNN, for example, a good observation is given in [1]-[3]. Traditionally CVNNs have been very successful in solving a number of real-world problems. We should mention such applications as detection of landmines [4], prediction of winds and their profiles [5], analysis of bio-medical images [6], prediction of oil production [7], frequency domain analysis of signals in EEG-based BCIs [8]. MLMVN is on the one hand a feedforward neural network, topologically identical to a multilayer perceptron (MLP). But on the other hand, MLVVN, being built from multi-valued neurons (MVNs) has its unique properties and important advantages over MLP. MLMVN was introduced in [9] as a 2-layer network. Then it was further developed [10] where MLMVN with an arbitrary number of hidden layers was introduced. Every particular property of MLMVN and its favorable distinctions over MLP are dictated by the utilization of the multi-valued neuron (MVN) as its essential unit. MVN was initially suggested in [11] as a k-valued threshold element and then re-introduced as a discrete MVN in [12]. MLMVN was effectively utilized in numerous applications. It was applied, for instance, for image deblurring through recognition of point-spread function and its specific parameters [13], long term time series prediction [7], analysis of signals in EEG-based BCIs [8], satellite information reversal for assurance of meteorological information profiles in the environment [15], solving various classification problems [3], [10], [16], and system identification [17]. MLMVN generalization capability in solving problems with discrete output, particularly classification and pattern recognition problems, was improved by a modified learning algorithm with soft margins [16]. To speed up a learning process and maintain simultaneously big learning sets and a high generalization capability, a batch learning algorithm was proposed in [17] and further developed in [18]. This algorithm as it is described in [18] was used in all experiments described in this paper. EEG is used to collect the data about brain electrical activity. Then analysis of these data can be used to discover a certain dysfunction of some groups of neurons in the brain. Particularly, EEG is used to diagnose epilepsy in its different stages and examine patients with this diagnosis in remission. In the context of computing, computer science and computer engineering, EEG is used in building brain/computer interfaces, which help people with disabilities caused by some brain dysfunctions to perform certain tasks. A seminal work on electrical activity in the brain was published in 1875 by Caton [19]. His ideas were significantly developed 50 years later by Berger [20], [21]. It was succeeded to him to detect electrical activity in the brain using special electrodes placed on the head. Corresponding signals were acquired and recorded using a galvanometer connected to these special electrodes. It was noticed that electrical activity of the brain may change, for example, when eyes are open or closed. With these developments, the presence of EEG signals was scientifically proven. EEG signals are used in diagnostics, controlling of the anesthesia stage during surgical procedures, studies of sleep disorders, sleep psychology, and investigation of migraine. These signals are measured using a BCI. It consists of special electrodes which are used for measuring the electrical activity of the brain from the head surface. Evaluation of EEGs is a specific job. It can typically be performed only by medical doctors whose area of specialization is EEG analysis. It is important to mention that EEG signals are not stable and they change continuously. They change their phases, frequencies and magnitudes. This makes interpretation of EEGs a challenging task. Medical doctors, depending on how different is their practical Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua