摘要
针对增量极限学习机(Convex incremental extreme learning machine,CI-ELM)的逼近能力分析问题,提出了一种基于Cauchy-Schwarz不等式的方法对CI-ELM算法的逼近阶进行定量分析.该方法针对激活函数g(x)所生成的函数序列定义了一个特殊的规范激活函数空间D,并在D上构造目标函数空间A_1(D),在Cauchy-Schwarz不等式基础上,利用分类讨论思想及数学归纳法对CI-ELM算法的逼近阶进行定量描述,从而初步揭示CI-ELM算法快速收敛的本质.结果证明,在目标函数空间A_1(D)上,CI-ELM逼近阶为O(n-1/2).
In order to analyze the approximation capability of CI-ELM from the quantitative point of view, an approach based on the Cauchy-Schwarz inequality is proposed to analyze the approximation order of CI-ELM algorithm. In terms of the function sequence generated by the activation function g（x）, this method defines a special specification activation function space D and helps to construct the target function space A（D） based on D. On the basis of Cauchy- Sehwarz inequality, classification is used to discuss ideas and mathematical induction is adoped for quantitative description of CI-ELM algorithm. The results show that in the target function space A1 （D）, the approximation order of CI-ELM is O（n-1/2） .
出处
《西安工程大学学报》
CAS
2015年第6期756-760,共5页
Journal of Xi’an Polytechnic University
基金
陕西省自然科学基金资助项目(2014JM1016)
