超核函数支持向量机

支持向量机是当前机器学习、模式识别和数据挖掘等领域的重要学习方法,核函数的构造是研究和应用支持向量机的关键问题.针对这一问题,提出了核函数构造的组合理论,定义了超核函数概念,并通过多项式组合现有核函数构造出一类超核函数.具体地,首先分析了一般核函数存在的过学习和欠学习现象,然后证明了组合理论构造的核函数的Mercer性质,并通过在仿真数据集和标准数据集上的对比实验,验证了超核函数的性能.理论分析和实验结果阐明了所提出的超核函数组合构造理论的合理性和有效性,开拓了模型选择组合方法的研究途径.

Support Vector Machines with Hyperkernel Functions

Support Vector Machines (SVM) provides an important approach to machine learning,pattern reorganization and data mining.Construction of kernel functions is the key both in SVM research and application.We proposed a combinatorial construction of hyperkernel functions for SVM,which is constructed by a polynomial combination of common kernels.We first analyzed the over-learning and under-learning phenomena of common kernel function.Then,we proved the Mercer condition of hyperkernels constructed by the proposed...