Margin setting algorithm for pattern classification via spheres
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Margin setting algorithm for pattern classification via spheres Yi Wang1 · W. David Pan2 · Jian Fu3 · Bingyang Wei4 Received: 16 May 2019 / Accepted: 8 June 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Margin setting algorithm (MSA) is a new sphere-based classification algorithm. It employs an artificial immune system approach to construct a number of hyperspheres that cover each class of a given set of data. To gain insights into the classification performance of MSA, it is the first work to analyze two important fundamental problems of MSA as a spherebased classifier. First, single sphere or multiple spheres are needed to achieve good classification performance in MSA? This problem was presented as sphere analysis, which was experimentally carried out on simulation data sets using Monte Carlo method. The results demonstrated that MSA employs a multiple-sphere strategy instead of one-sphere strategy as its decision boundaries. This strategy allows MSA to achieve lower probabilities of classification error rate. Second, how to adapt the location and size of the hypersphere to achieve good classification performance? This problem was presented as adaption analysis, which was experimentally carried out on real-world data sets compared to the support vector machine and the artificial neural network. The results demonstrated that MSA employs an artificial immune system approach to optimize the locations of the hyperspheres and to shrink the radius of the hypersphere in a certain range using margin as an algorithm parameter. Overall, computational results indicate the advantages of MSA in classification performance. Keywords Sphere-based classification · Margin setting · Hypersphere · Multi-sphere decision boundary
1 Introduction The most widely used algorithms in pattern classification partition the input-data space into several convex sets, so that convex sets cover samples of one class against other classes to represent dispersion of each class data. The convex sets can be boxes, spheres, half-spaces, cylinders or * Yi Wang [email protected] W. David Pan [email protected] Jian Fu [email protected] Bingyang Wei [email protected] 1
Electrical and Computer Engineering Department, Manhattan College, Riverdale, NY 10471, USA
2
Electrical and Computer Engineering Department, University of Alabama in Huntsville, Huntsville, AL 35899, USA
3
Electrical Engineering and Computer Science Department, Alabama A&M University, Normal, AL 35762, USA
4
Texas Christian University, Fort Worth, TX 76129, USA
convex hulls [1, 2]. For an n-dimensional input-data space, spheres are called hypersphere, which is one of the simple boundary forms. Sphere decision boundary is constructed by comparing the radius of sphere with the Euclidean distance between the unknown data sample and a fixed point, i.e., the centroid of sphere. Based on the comparison results, i.e., whether the Euclidean distance is larger or small than the radius, the samples can be classified into different cla
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