This work focuses on non-linear characterization of 61-channel electroencephalogram (EEG) signal for detecting alcoholics using ranked Approximate Entropy (ApEn) parameters. Significant channels that contribute to the detection of alcoholism are selected by ranking the ApEn features based on ANOVA test. In order to classify alcoholics from control, the ranked feature set is applied to two non-linear classifiers, namely Back Propagation Neural Network (BPNN) and Support Vector Machine (SVM) Classifiers respectively. The performance of the classifiers is evaluated in terms of classification accuracy as well as computational processing time. Experimental results reveal that the BPNN classifier with 40 hidden neurons and SVM classifier with a polynomial kernel of order 3 perform with an accuracy of 90% with only 32 ranked ApEn coefficients.