基于后验概率的支持向量机吴高巍.pdfVIP

ISSN 1000-1239/CN 11-1777/TP Journal of Computer Research and Development 2(2):196 ～ 202, 2005 1 2, 3 2 吴高巍 　陶　卿 　王　珏 1 (　　100080) 2 (　　100080) 3 (　　230031) (w ugaowei @) Support Vector Machines Based on Posteriori Probability 1 2, 3 2 Wu Gaowei , Tao Qing , and Wang Jue 1 (Intelligent InformanceProcessing Open Laboratory, Instituteof Computing Technology , Chinese Academy of Sciences, Beijing 100080) 2 (Laboratory of Computer System and IntelligenceScience, Institute of Automation, Chinese Academy of Sciences, Beij ing 100080) 3 (2 nd Department, Ne Star Research Inst of Applied Tech, Hef ei 230031) Abstract　To solve uncertain classification problem, an SVM (support vector machine)is trained to behave like a Bayesian optimal classifier based on the training data.The idea is to weigh each unbalanced training sample by a posteriori probability.A w hole framework of posteriori probability support vector machine (PPSVM )is presented and SVM is reformulated into PPSVM.The linear separability, margin, optimal hyperplane and soft margin algorithms are discussed.A new optimization problem is obtained and a new definition of support vector is given.In fact, PPSVM is motivated by statistical learning theory and is an extension of regular SVM.An empirical method is also proposed for determining the posteriori probability. Tw o artificial examples show that PPSVM formulation is reasonable if the class-conditional probability is know n, and some real experiments demonstrate that the weighted data cases by some empirical methods can produce better results than regular SVM. Key words　support vector machines;classification;posterior probability;margin;maximal margin algo- rithm;uncertain classification problem 　　在支持向量机(support vector machines, SVM )中, 训练样本总是具有明确的类别信息, 而对