Background: K-complex detection plays a significant role in the field of sleep research. However, manual annotation for electroencephalography (EEG) recordings by visual inspection from experts is time-consuming and subjective. Therefore, there is a necessity to implement automatic detection methods based on classical machine learning algorithms. However, due to the complexity of EEG signal, current feature extraction methods always produce low relevance to k-complex detection, which leads to a great performance loss for the detection. Hence, finding compact yet effective integrated feature vectors becomes a crucially core task in k-complex detection. Method: In this paper, we first extract multi-domain features based on time, spectral analysis, and chaotic theory. Those features are extracted from a 0.5-s EEG segment, which is obtained using the sliding window technique. As a result, a vector containing twenty-two features is obtained to represent each segment. Next, we explore several feature selection methods and compare their performance in detecting k-complex. Based on the analysis of the selected features, we identify compact features which are fewer than twenty-two features and deemed as relevant and proceeded to the next step. Additionally, three classical classifiers are employed to evaluate the performance of the feature selection models. Results: The results demonstrate that combining different features significantly improved the k-complex detection performance. The best performance is achieved by applying the feature selection method, which results in an accuracy of 93.03% (Formula presented.) 7.34, sensitivity of 93.81% (Formula presented.) 5.62%, and specificity 94.13 (Formula presented.) 5.81, respectively, using a smaller number of the combined feature sets. Conclusion: The proposed method in this study can serve as an efficient tool for the automatic detection of k-complex, which is useful for neurologists or doctors in the diagnosis of sleep research.