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MATHEMATICAL
TECHNIQUES FOR STUDY OF
EEG DATA RECORDED DURING MEDITATION D. Narayana Dutt Dept.
of Electrical Communication Engineering Indian
Institute of Science |
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Meditation is
considered to be an altered state of consciousness associated with heightened
cognitive functions and transcendental experiences. The neural dynamics in
meditative states needs to be explored and an objective analysis of such states
is required. Here, we have investigated the dimensional complexity of electroencephalogram
(EEG) signals from the brain of subjects in yogic meditation. Several
channels of EEG have been analyzed in terms of compressed spectral array
(CSA), running fractal dimension and running attractor dimension during the
process of meditation. The CSA yields some interesting features. The running
fractal plots show low average fractal dimension values during pre-meditative
and post-meditative periods. During meditation there is an increase in the
average fractal dimension value. The attractor dimension values also show
changes. As the meditation progresses the average attractor dimension rises
to a value which is more than that for the premeditative period. It shows a
decline during some stages of meditation. The results indicate that the
attractor dimension estimation is more effective in depicting the dynamics of
the brain in a highly complex state. The investigation reveals that chaotic
dynamics provides a mechanism for low dimensional control of neuronal
oscillations in meditation Next, we have
studied the efficacy of neural network approach in differentiating various
levels of consciousness using EEG signals. We considered 60 segments of
premeditation data, 140 segments of meditation data, 140 segments of deep
meditation data and 60 segments of post meditation data. We have chosen 8
features as input to the neural networks. The features we have chosen are
mean, variance, fractal dimension, complexity measure, and powers in alpha,
beta, theta and delta waves. Four classification algorithms were compared
viz., k-neighbors, RBF networks, Support vector machines (SVM) and back
propagation networks for different set of features. The obtained accuracies
for the back propagation network, RBF network units and support vector
machine with RBF kernel are higher than for k-neighbors. We are able to
attain optimum accuracy of 99.6% with SVM in case of two-category problem
(Meditation and Pre-meditation), 99.6% with SVM in case of three-category
problem (Pre-meditation, Meditation and Post meditation) and 99.38% with SVM
in case of four-category problem (Pre-meditation, Meditation, Deep meditation and Post meditation). Thus this work has
shown the feasibility of the use of neural networks in the classification of
EEG meditation data. In summary, this
work has demonstrated the efficacy of mathematical techniques in establishing
that meditative state is indeed a well defined and distinct state of
consciousness where clear changes are observed in EEG during meditation. The
fact that an automated method like neural network approach can differentiate
such states from other states clearly shows that there is no human bias
involved in such studies. |