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July  2015, 11(3): 921-932. doi: 10.3934/jimo.2015.11.921

## Clustering based polyhedral conic functions algorithm in classification

 1 Department of Industrial Engineering, Faculty of Engineering, Anadolu University, Eskisehir, 26555, Turkey 2 Vitra, Eczacibasi Yapi Gerecleri, 11300 Bilecik, Turkey

Received  October 2013 Revised  June 2014 Published  October 2014

In this study, a new algorithm based on polyhedral conic functions (PCFs) is developed to solve multi-class supervised data classification problems. The $k$ PCFs are constructed for each class in order to separate it from the rest of the data set. The $k$-means algorithm is applied to find vertices of PCFs and then a linear programming model is solved to calculate the parameters of each PCF. The separating functions for each class are obtained as a pointwise minimum of the PCFs. A class label is assigned to the test point according to its minimum value over all separating functions. In order to demonstrate the performance of the proposed algorithm, it is applied to solve classification problems in publicly available data sets. The comparative results with some mainstream classifiers are presented.
Citation: Gurkan Ozturk, Mehmet Tahir Ciftci. Clustering based polyhedral conic functions algorithm in classification. Journal of Industrial & Management Optimization, 2015, 11 (3) : 921-932. doi: 10.3934/jimo.2015.11.921
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