乘积匹配多项式的存在性

Existence of product-matching polynomials

假若一个以点积为自变量的多项式不是再生核,则它无法在机器学习的核方法中使用.解决此问题的办法之一是匹配另外一个点积的多项式,使两者乘积成为再生核.在一定条件下,通过解一系列的不等式,得到匹配多项式存在的充分必要条件,并探讨与此条件相关的数列和生成函数列的性质.

If a polynomial with the dot product as its independent variable is not a reproducing kernel, there will be no way to use it in kernel method for machine learning. One of the dealing methods is matching it with another dot-product polynomial such that their product is areproducing kernel. Under certain conditions and by means of solving a sequence of inequality systems, a sufficient and necessary condition of the existence of the matching polynomials is found and the sequence relevant to this condition and the properties of the generated function sequence are explored.