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Sleep stage identification is the first step in modern sleep disorder diagnostics process. K-complex is an indicator for the sleep stage 2. However, due to the ambiguity of the translation of the medical standards into a computer-based procedure, reliability of automated K-complex detection from the EEG wave is still far from expectation. More specifically, there are some significant barriers to the research of automatic K-complex detection. First, there is no adequate description of K-complex that makes it difficult to develop automatic detection algorithm. Second, human experts only provided the label for whether a whole EEG segment contains K-complex or not, rather than individual labels for each subsegment. These barriers render most pattern recognition algorithms inapplicable in detecting K-complex. In this paper, we attempt to address these two challenges, by designing a new feature extraction method that can transform visual features of the EEG wave with any length into mathematical representation and proposing a hybrid-synergic machine learning method to build a K-complex classifier. The tenfold cross-validation results indicate that both the accuracy and the precision of this proposed model are at least as good as a human expert in K-complex detection.