Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (6): 1611-1619.

### Piecewise Combination of Hyper-Sphere Support Vector Machine for Multi-Class Classification Problems

Shuang Liua,*, Peng Chenb, Jiayi Lia, Hui Yanga, and Niko Lukačc

1. a School of Computer Science and Engineering, Dalian Minzu University, Dalian, 116600, China
b Department of Software Engineering, Dalian Neusoft University of Information, Dalian, 116023, China
c Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, SI-2000, Slovenia
• Submitted on  ;
• Contact: * E-mail address: liushuang@dlnu.edu.cn
• About author:Shuang Liu received her Ph.D. in traffic information engineering and control from Dalian Maritime University, China. She is currently an associate professor at Dalian Minzu University, China. Her current research interests include machine learning and image processing;Peng Chen is currently a professor at Dalian Neusoft University of Information, China. His research interests include machine learning, collision avoidance, and intelligent information processing;Jiayi Li is currently a postgraduate candidate at Dalian Minzu University, China. Her research interests include deep learning and big data;Hui Yang is currently a postgraduate candidate at Dalian Minzu University, China. His research interests include deep learning and big data;Niko Lukač obtained his Ph.D. in computer science in 2016 from Maribor University. He is currently a researcher in the Faculty of Electrical Engineering and Computer Science at the University of Maribor, Slovenia.
• Supported by:
This work is partially supported by the National Nature Science Foundation of Liaoning Province (No. 2015020099) and the National Natural Science Foundation (No. 71303031).

Abstract: Hyper-sphere Support vector machine (SVM) is a widely used machine learning method for multi-class classification problems such as image recognition, text classification, or handwriting recognition. In most cases, only one hyper-sphere optimization problem is computed to solve the problem. However, there are many complex applications with complicated data distributions. In these cases, the computation cost will be increased with unsatisfied classification results if only one support vector machine is adopted as the classification decision rule. To achieve good classification performance, a piecewise combination of the hyper-sphere support vector machine is put forward in this paper based on the analysis of the data sample distribution. First, statistical analysis is adopted for the original data. Then, the k-means cluster algorithm is introduced to compute cluster centers for different classes of the data. For the n classes classification problem, m (m > n) hyper-spheres are computed to solve the objective problems based on the number of data centers. For simple sphere-distribution and locally linearly separable distribution cases, the minimum enclosing and maximum excluding support vector machine and the combination of hyper-sphere support vector machine are defined. Experimental results show that different support vector machines for different data distributions will improve the final classification performance.