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Currently, methods of combined classification are the focus of intense research. A properly designed group of combined classifiers exploiting knowledge gathered in a pool of elementary classifiers can successfully outperform a single classifier. There are two essential issues to consider when creating combined classifiers: how to establish the most comprehensive pool and how to design a fusion model that allows for taking full advantage of the collected knowledge. In this work, we address the issues and propose an AdaSS+, training algorithm dedicated for the compound classifier system that effectively exploits local specialization of the elementary classifiers. An effective training procedure consists of two phases. The first phase detects the classifier competencies and adjusts the respective fusion parameters. The second phase boosts classification accuracy by elevating the degree of local specialization. The quality of the proposed algorithms are evaluated on the basis of a wide range of computer experiments that show that AdaSS+ can outperform the original method and several reference classifiers.

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