普适性核度量标准比较研究

核方法是一类应用较为广泛的机器学习算法,已被应用于分类、聚类、回归和特征选择等方面.核函数的选择与参数优化一直是影响核方法效果的核心问题,从而推动了核度量标准,特别是普适性核度量标准的研究.对应用最为广泛的5种普适性核度量标准进行了分析与比较研究,包括KTA,EKTA,CKTA,FSM和KCSM.发现上述5种普适性度量标准的度量内容为特征空间中线性假设的平均间隔,与支持向量机最大化最小间隔的优化标准存在偏差.然后,使用模拟数据分析了上述标准的类别分布敏感性、线性平移敏感性、异方差数据敏感性,发现上述标准仅是核度量的充分非必要条件,好的核函数可能获得较低的度量值.最后,在9个UCI数据集和20Newsgroups数据集上比较了上述标准的度量效果,发现CKTA是度量效果最好的普适性核度量标准.

Comparative Study of Universal Kernel Evaluation Measures

Kernel method is a common machine learning algorithm used in classification, clustering, regression and feature selection. Kernel selection and kernel parameter optimization are the crucial problems which impact the effectiveness of kernel method, and therefore motive the research on kernel evaluation measure, especially universal kernel evaluation measure. Five widely used universal kernel evaluation measures, including KTA, EKTA, CKTA, FSM and KCSM, are analyzed and compared. It is found that the evaluation object of five universal kernel evaluation measures mentioned above is average margin of a linear hypothesis in feature space, which has bias against the SVM optimization criterion to maximize minimum margin. Then, this study applies synthetic data to analyze the class distribution sensitivity, linear translation sensitivity, and heteroscedastic data sensitivity. It also concludes that the measures mentioned above are only the unnecessary and sufficient condition of kernel evaluation, and good kernel can achieve low evaluation value. Finally, comparing the evaluation result of the measures mentioned above on 9 UCI data sets and 20 Newsgroups data set suggests that CKTA is the best universal kernel evaluation measure.