分形理论下支持向量机核函数选择

Research on Selection of Kernel Function of SVM under Fractal Theory

支持向量机(support vector machine,SVM)是一种基于核的机器学习方法,不同的核函数对SVM的性能影响显著,如何针对具体问题获得一种有效的核函数选择方法成为SVM研究领域的一个重要问题。目前核函数选取仍是一个开放性的问题,存在着一系列的偶然性和局限性。而针对相对复杂问题时,使用何种类型的单一基核函数难以反映出其分布特征。因此,提出一种基于分形理论的核函数选择方法,在考虑不同核函数度量特征的同时,结合具体问题样本分布特征合理构造或选择核函数类型,并通过数据仿真以及相似性对比验证了算法的合理性。

Support vector machine (SVM) is a kernel-based machine learning method.Different kernel functions have a significant impact on the performance of SVM.How to obtain an effective kernel function selection method for specific problems has become an important issue in the field of SVM research.At present,the selection of kernel function is still an open issue,with a series of contingencies and limitations.However,it is difficult to reflect the distribution characteristics of any type of single basis kernel function for relatively complex problems.Therefore,a kernel function selection method based on the fractal theory is proposed.While considering the metric features of different kernel functions,the core function type can be reasonably constructed or selected based on the sample distribution characteristics of specific problems.The rationality of the algorithm was verified by data simulation and similarity comparison.