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Electroencephalography (EEG) signals are considered one of the oldest techniques for detecting disorders in medical signal processing. However, brain complexity and the non-stationary nature of EEG signals represent a challenge when applying this technique. The current paper proposes new geometrical features for classifi cation of seizure (S) and seizure-free (SF) EEG signals with respect to the Poincaré pattern of discrete wavelet transform (DWT) coeffi cients. DWT decomposes EEG signal to four levels, and thus Poincaré plot is shown for coeffi cients. Due to patterns of the Poincaré plot, novel geometrical features are computed from EEG signals. The computed features are involved in standard descriptors of 2-D projection (STD), summation of triangle area using consecutive points (STA), as well as summation of shortest distance from each point relative to the 45-degree line (SSHD), and summation of distance from each point relative to the coordinate center (SDTC). The proposed procedure leads to discriminate features between S and SF EEG signals. Thereafter, a binary particle swarm optimization (BPSO) is developed as an appropriate technique for feature selection. Finally, k-nearest neighbor (KNN) and support vector machine (SVM) classifi ers are used for classifying features in S and SF groups. By developing the proposed method, we have archived classifi cation accuracy of 99.3 % with respect to the proposed geometrical features. Accordingly, S and SF EEG signals have been classifi ed. Also, Poincaré plot of SF EEG signals has more regular geometrical shapes as compared to S group. As a fi nal remark, we notice that the Poincaré plot of coeffi cients in S EEG signals has occupied more space as compared to SF EEG signals (Tab. 3, Fig. 11, Ref. 57).

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