Abstract
Support vector machines (SVMs) are a well-known classifier due to their superior classification performance. They are defined by a hyperplane, which separates two classes with the largest margin. In the computation of the hyperplane, however, it is necessary to solve a quadratic programming problem. The storage cost of a quadratic programming problem grows with the square of the number of training sample points, and the time complexity is proportional to the cube of the number in general. Thus, it is worth studying how to reduce the training time of SVMs without compromising the performance to prepare for sustainability in large-scale SVM problems. In this paper, we proposed a novel data reduction method for reducing the training time by combining decision trees and relative support distance. We applied a new concept, relative support distance, to select good support vector candidates in each partition generated by the decision trees. The selected support vector candidates improved the training speed for large-scale SVM problems. In experiments, we demonstrated that our approach significantly reduced the training time while maintaining good classification performance in comparison with existing approaches.
Highlights
Support vector machines (SVMs) [1] have been a very powerful machine learning algorithm developed for classification problems, which works by recognizing patterns via kernel tricks [2]
Its nonlinear separation can be achieved via kernel functions, which map the input space to a high-dimensional space, called feature space where optimal separating hyperplane is determined in the feature space
In order to cope with large-scale SVM problems, we propose a novel selection method for support vector candidates using a combination of tree decomposition and relative support distance
Summary
Support vector machines (SVMs) [1] have been a very powerful machine learning algorithm developed for classification problems, which works by recognizing patterns via kernel tricks [2].Because of its high performance and great generalization ability compared with other classification methods, the SVM method is widely used in bioinformatics, text and image recognition, and finances, to name a few. The method finds a linear boundary (hyperplane) that represents the largest margin between two classes (labels) in the input space [3,4,5,6]. It can be applied to linear separation and nonlinear separation using kernel functions. Its nonlinear separation can be achieved via kernel functions, which map the input space to a high-dimensional space, called feature space where optimal separating hyperplane is determined in the feature space. The hyperplane in the feature space, which achieves a better separation of training data, is translated to a nonlinear boundary in the original space [7,8]. The kernel trick is used to associate the kernel function with the mapping function, bringing forth a nonlinear separation in the input space
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