K-complexes identification is a challenging task in sleep research. The detection of k-complexes in electroencephalogram (EEG) signals based on visual inspection is time-consuming, prone to errors, and requires well-trained knowledge. Many existing methods for k-complexes detection rely mainly on analysing EEG signals in time and frequency domains. In this study, an efficient method is proposed to detect k-complexes from EEG signals based on the fractal dimension (FD) of time-frequency (T-F) images coupled with undirected graph features. Firstly, the EEG signal is partitioned into smaller segments using a sliding window technique. Each EEG segment is passed through a spectrogram of short time Fourier transform (STFT) to obtain T-F images. Secondly, the box-counting method is applied to each T-F image to estimate and discover the FDs in EEG signals. A vector of FD features are extracted from each T-F image and then mapped into an undirected graph. The structural properties of the graphs are used as the representative features of the original EEG signals for the input of a least square support vector machine (LS-SVM) classifier. Key graphic features are extracted from the undirected graphs. The extracted graph features are forwarded to the LS-SVM for classification. To investigate the classification ability of the proposed feature extraction combined with the LS-SVM classifier, the extracted features are also forwarded to a k-means classifier for comparison. The proposed method is compared with several existing k-complexes detection methods in which the same datasets were used. The findings of this study shows that the proposed method yields better classification results than other existing methods in the literature. An average accuracy of 97% for the detection of the k-complexes is obtained using the proposed method. The proposed method could lead to an efficient tool for the scoring of automatic sleep stages which could be useful for doctors and neurologists in the diagnosis and treatment of sleep disorders and for sleep research

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