Çok gruplu veri sınıflandırma için tamsayı karışık programlamaya dayalı çok boyutlu kutu ile çevreleme yaklaşımı

Data classification is an important data mining problem that aims to determine the membership of different instances to a number of different sets. Traditional approaches that are based on partitioning the data sets into two groups need some modifications for multi-class data classification problems. These modifications affect the efficiency and make the models more complex. In this thesis, a novel mixed integer programming based hyper-box enclosure approach is presented for multi-class data classification problems. In order to deal with large data sets, a three-stage mathematical programming based approach is developed for training part analysis of hyper-box enclosure method. Training set is preprocessed to identify the observations that are more difficult to classify, and seed finding and sub grouping algorithms are applied in the first stage. Then, optimization model is formulated considering these observations and seeds. Finally, assignments of non-problematic instances, intersection elimination and box combination algorithms are carried out. After training analysis with this three stage approach, the efficiency of the method is tested by the simple distance based testing algorithm. The efficiency of the proposed three-stage method is tested on two separate benchmark problems; the protein folding type prediction problem and the UCI Repository data sets. The computational results on the illustrative example and the benchmark problems show the accuracy of the proposed method.