In this paper, we detect the occurrence of epileptic seizures in patients as well as activities namely stand, walk, and exercise in healthy persons, leveraging EEG (electroencephalogram) signals. Using Hilbert vibration decomposition (HVD) on non-linear and non-stationary EEG signal, we obtain multiple monocomponents varying in terms of amplitude and frequency. After decomposition, we extract features from the monocomponent matrix of the EEG signals. The instantaneous amplitude of the HVD monocomponents varies because of the motion artifacts present in EEG signals. Hence, the acquired statistical features from the instantaneous amplitude help in identifying the epileptic seizures and the normal human activities. The features selected by correlation-based Q-score are classified using an LSTM (Long Short Term Memory) based deep learning model in which the feature-based weight update maximizes the classification accuracy. For epilepsy diagnosis using the Bonn dataset and activity recognition leveraging our Sensor Networks Research Lab (SNRL) data, we achieve testing classification accuracies of 96.00% and 83.30% respectively through our proposed method.