# Piecewise Combination of Hyper-Sphere Support Vector Machine for Multi-Class Classification Problems
##### Volume 15, Number 6, June 2019, pp. 1611-1619 DOI: 10.23940/ijpe.19.06.p12.16111619
## Shuang Liu^{a}, Peng Chen^{b}, Jiayi Li^{a}, Hui Yang^{a}, and Niko Lukač^{c}
^{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 March 20, 2019; Revised on April 4, 2019; Accepted on June 8, 201)
## 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.
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