基于正交多项式核函数方法

Review of Chebyshev Kernel Functions

针对实际工程中小样本数据的稀疏性、分布特征不明显等问题,分析了现有的一些方法并指出了现有方法存在的问题,重点讨论了一类基于切比雪夫多项式的核方法。由于切比雪夫多项式的正交性,使得这些核函数在高维特征空间能得到更优的超平面。通过实验测试了这一类核函数的泛化性能以及学习效率。证明它们比其它的核函数需要更少的支持向量并能保证更好的学习性能。最后论文讨论了这类核函数方法存在的问题,并指出切比雪夫多项式核函数在解决小样本回归问题时具有很大的潜力,值得进一步研究。

In practical engineering ,small-scale data sets are usually sparse and contaminated by noise. Analyze some new methods and their problem. Furthermore, discuss the Chebyshev kernel functions which were proposed recently. Because of the orthogonality of Cbeby- shev polynomials,the new kernels can find the best hyperplane in the feature space. To evaluate the perfomaance of the new kernels,ap- plied it to learn some benchmark data sets, and compared them with other conventional SVM kernels. The experiment results show that the Chebyshev kernels have excellent generalization performance and prediction accuracy, and do not cost much less support vectors compared with other kernels. Point out the problem of the new kernels and the research direction.