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Epilepsy is one of the most common brain disorders, but the dynamical transitions to neurological dysfunctions of epilepsy are not well understood in current neuroscience research. Uncontrolled epilepsy poses a significant burden to society due to associated healthcare cost to treat and control the unpredictable and spontaneous occurrence of seizures. The objective of this study is to develop and present a novel classification technique that is used to classify normal and abnormal (epileptic) brain activities through quantitative analyses of electroencephalogram (EEG) recordings. Such technique is based on the integration of sophisticated approaches from data mining and signal processing research (i.e., chaos theory, k-nearest neighbor, and statistical time series analysis). The proposed technique can correctly classify normal and abnormal EEGs with a sensitivity of 81.29% and a specificity of 72.86%, on average, across ten patients. Experimental results suggest that the proposed technique can be used to develop abnormal brain activity classification for detecting seizure precursors. Success of this study demonstrates that the proposed technique can excavate hidden patterns/relationships in EEGs and give greater understanding of brain functions from a system perspective, which will advance current diagnosis and treatment of epilepsy.