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The ECOC technique is a powerful tool to learn and combine multiple binary learners for multi-class classification. It generally involves three steps: coding, dichotomizers learning, and decoding. In previous ECOC methods, the coding step and the dichotomizers learning step are usually performed independently. This simplifies the learning problem but may lead to unsatisfactory decoding results. To solve this problem, we propose a novel model for learning the ECOC matrix and dichotomizers jointly from data. We formulate the model as a nonlinear programming problem and develop an efficient alternating minimization algorithm to solve it. Specifically, for fixed ECOC matrix, our model is decomposed into a group of mutually independent quadratic programming problems; while for fixed dichotomizers, it is a difference of convex functions problem and can be easily solved using the concave--convex procedure algorithm. Our experimental results on ten data sets from the UCI machine learning repository demonstrated the advantage of our model over state-of-the-art ECOC methods. [ABSTRACT FROM AUTHOR]