One-class classification problem aims to identify elements of a specific class among all other elements. This problem has been extensively studied in the last decade and the developed methods were applied to a large number of different problems, such as outlier detection, natural language processing, fraud detection, and many others. In this work, we developed a new semi-supervised one-class classification algorithm which assumes that the class is linearly separable from other elements. We proved theoretically that the class is linearly separable if and only if it is maximal by probability within the sets of elements with the same mean. Furthermore, we constructed an algorithm for identifying such linearly separable class based on linear programming. We considered three application cases including an assumption of linear separability of the class, Gaussian distribution, and the case of linear separability in the transformed space of kernel functions. Finally, we examined the work of the proposed algorithm on the USPS dataset and analyzed the relationship of its performance and the size of the initially labeled sample.
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