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In this paper, the classical binary classification problem is investigated. Necessary and sufficient criterion is presented to guarantee the linear binary separability of the training data in the Euclidean normed space. A suitable hyperplane that correctly classifies the training data is also constructed provided that the necessary and sufficient is satisfied. Based on the main result, we offer an easy-to-check criterion for the linear binary separability of the training set. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

New Criteria for the Linear Binary Separability in the Euclidean Normed Space