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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

Gurkan Ozturk 1, and  Mehmet Tahir Ciftci 2,

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.
Keywords: computational learning theory., polyhedral conic cunctions, Classification, linear programming, K-means.
Mathematics Subject Classification: Primary: 68Q32, 46N10; Secondary: 97R5.
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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show all references

References:
[1]

Journal of Optimization Theory and Applications, 112 (2002), 265-293. doi: 10.1023/A:1013649822153.  Google Scholar

[2]

Journal of Convex Analysis, 21 (2014), 001-028. Google Scholar

[3]

K. Bache and M. Lichman, UCI machine learning repository, 2013., URL , ().   Google Scholar

[4]

Optimization Methods and Software, 20 (2005), 277-296. doi: 10.1080/10556780512331318263.  Google Scholar

[5]

Applied Optimization, 99 (2005), 175-207. doi: 10.1007/0-387-26771-9_6.  Google Scholar

[6]

Journal of Industrial and Management Optimization, 2 (2006), 319-338. Google Scholar

[7]

TOP, 21 (2013), 3-24. ISSN 1134-5764. doi: 10.1007/s11750-011-0241-5.  Google Scholar

[8]

Data Mining and Knowledge Discovery, 2 (1998), 121-167. Google Scholar

[9]

Optimization Methods and Software, 21 (2006), 527-540. doi: 10.1080/10556780600723252.  Google Scholar

[10]

SIGKDD Explorations, 11 (2009), 10-18. ISSN 1931-0145. doi: 10.1145/1656274.1656278.  Google Scholar

[11]

Optimization, 58 (2009), 521-534. doi: 10.1080/02331930902928310.  Google Scholar

[12]

SIAM J. on Optimization, 20 (2009), 1591-1619. ISSN 1052-6234. doi: 10.1137/070694089.  Google Scholar

[13]

SIAM Journal on Optimization, 20 (2009), 841-855. doi: 10.1137/080738106.  Google Scholar

[14]

PhD thesis, Eskisehir Osmangazi University, Institute of Scince, 6 2007. (in Turkish). Google Scholar

[15]

GAMS Development Corporation, Washington, DC, 2013. URL http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf. Google Scholar

[16]

Journal of Industrial and Management Optimization, 1 (2005), 465-476. doi: 10.3934/jimo.2005.1.465.  Google Scholar

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