Posterior probability support vector Machines for unbalanced data
Posterior probability support vector Machines for unbalanced data
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DOI：
10.1109/tnn.2005.857955
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发表时间：
2005-11
影响因子：
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通讯作者：
Qing Tao;Gao-wei Wu;Fei-Yue Wang;Jue Wang
中科院分区：
文献类型：
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作者：
Qing Tao;Gao-wei Wu;Fei-Yue Wang;Jue Wang
本文提出了一个用于加权训练样本的后验概率支持向量机（PPSVM）的完整框架，使用修改后的风险、线性可分离性、边际和最优超平面的概念。在此框架内，提出了针对不平衡分类问题的新优化问题，并建立了支持向量的新概念。此外，获得了具有可解释参数/spl nu/的软PPSVM，类似于Scho/spl uml/lkopf等人开发的/spl nu/-SVM，并提出了一种确定后验概率的经验方法作为确定/spl nu/的新方法。 PPSVM 分类器的主要优点在于，它在不知道分布的情况下更接近贝叶斯最优。为了验证所提出的方法，使用两个综合分类示例来说明 PPSVM 的逻辑正确性及其与常规 SVM 和贝叶斯方法的关系。进行了其他几个分类实验来证明 PPSVM 的性能在某些情况下优于常规 SVM。与模糊支持向量机（FSVM）相比，所提出的 PPSVM 是基于统计学习理论的常规 SVM 的自然分析扩展。
This paper proposes a complete framework of posterior probability support vector machines (PPSVMs) for weighted training samples using modified concepts of risks, linear separability, margin, and optimal hyperplane. Within this framework, a new optimization problem for unbalanced classification problems is formulated and a new concept of support vectors established. Furthermore, a soft PPSVM with an interpretable parameter /spl nu/ is obtained which is similar to the /spl nu/-SVM developed by Scho/spl uml/lkopf et al., and an empirical method for determining the posterior probability is proposed as a new approach to determine /spl nu/. The main advantage of an PPSVM classifier lies in that fact that it is closer to the Bayes optimal without knowing the distributions. To validate the proposed method, two synthetic classification examples are used to illustrate the logical correctness of PPSVMs and their relationship to regular SVMs and Bayesian methods. Several other classification experiments are conducted to demonstrate that the performance of PPSVMs is better than regular SVMs in some cases. Compared with fuzzy support vector machines (FSVMs), the proposed PPSVM is a natural and an analytical extension of regular SVMs based on the statistical learning theory.