基于支撑域的单分类器和密度估计的本质关系

摘要

单类支持向量机和支持向量数据描述是两种流行的基于支撑域的单分类器.为揭示采用高斯核后他们与密度估计之间的关系,首先将基于支撑域的单分类器统一到密度估计的框架下;其次证明了基于支撑域的单分类器诱导的密度估计和真实密度一致,同时也能减小积分平方误差.最后通过人工数据集实验验证了上述关系.%One-class support vector machine (OCSVM) and support vector data description (SVDD) are two main domain-based one-class (kernel) classifiers. To reveal their relationship with density estimation in the case of the Gaussian kernel, OCSVM and SVDD are firstly unified into the framework of kernel density estimation, and the essential relationship between them is explicitly revealed. Then the result proves that the density estimation induced by OCSVM or SVDD is in agreement with the true density. Meanwhile, it can also reduce the integrated squared error (ISE). Finally, experiments on several simulated datasets verify the revealed relationships.