Liu Yufeng, Wu Yichao, He Qinying
Department of Statistics and Operations Research, Carolina Center for Genome Sciences, University of North Carolina, Chapel Hill, NC 27599 (
Stat Interface. 2010 Oct 1;3(4):465-476. doi: 10.4310/sii.2010.v3.n4.a5.
The Support Vector Machines (SVM) has been an important classification technique in both machine learning and statistics communities. The robust SVM is an improved version of the SVM so that the resulting classifier can be less sensitive to outliers. In many practical problems, it may be advantageous to use different weights for different types of misclassification. However, the existing RSVM treats different kinds of misclassification equally. In this paper, we propose the weighted RSVM, as an extension of the standard SVM. We show that surprisingly, the cost-based weights do not work well for weighted extensions of the RSVM. To solve this problem, we propose a novel utility-based weights for the weighted RSVM. Both theoretical and numerical studies are presented to investigate the performance of the proposed weighted multicategory RSVM.
支持向量机（SVM）一直是机器学习和统计学领域中的一种重要分类技术。鲁棒支持向量机（RSVM）是支持向量机的改进版本，使得所得分类器对异常值的敏感度降低。在许多实际问题中，对不同类型的错误分类使用不同的权重可能会更有利。然而，现有的鲁棒支持向量机对不同类型的错误分类一视同仁。在本文中，我们提出了加权鲁棒支持向量机，作为标准支持向量机的扩展。我们令人惊讶地发现，基于成本的权重在鲁棒支持向量机的加权扩展中效果不佳。为了解决这个问题，我们为加权鲁棒支持向量机提出了一种基于效用的新型权重。我们进行了理论和数值研究，以考察所提出的加权多类鲁棒支持向量机的性能。
