基于神经正切核的多核学习方法

多核学习方法是一类重要的核学习方法，但大多数多核学习方法存在如下问题：多核学习方法中的基核函数大多选择传统的具有浅层结构的核函数，在处理数据规模大且分布不平坦的问题时表示能力较弱；现有的多核学习方法的泛化误差收敛率大多为O\left(\mathrm{1}/\sqrt[]{n}\right)，收敛速度较慢。为此，提出了一种基于神经正切核（NTK）的多核学习方法。首先，将具有深层次结构的NTK作为多核学习方法的基核函数，从而增强多核学习方法的表示能力。然后，根据主特征值比例度量证明了一种收敛速率可达O\left(\mathrm{1}/n\right)的泛化误差界；在此基础上，结合核对齐度量设计了一种全新的多核学习算法。最后，在多个数据集上进行了实验，实验结果表明，相比Adaboost和K近邻（KNN）等分类算法，新提出的多核学习算法具有更高的准确率和更好的表示能力，也验证了所提方法的可行性与有效性。

Multi-kernel learning method based on neural tangent kernel

Multi-kernel learning method is an important type of kernel learning method， but most of multi-kernel learning methods have the following problems： most of the basis kernel functions in multi-kernel learning methods are traditional kernel functions with shallow structure， which have weak representation ability when dealing with the problems of large data scale and uneven distribution； the generalization error convergence rates of the existing multi-kernel learning methods are mostly O\left(\mathrm{1}/\sqrt[]{n}\right)， and the convergence speeds are slow. Therefore， a multi-kernel learning method based on Neural Tangent Kernel （NTK） was proposed. Firstly， the NTK with deep structure was used as the basis kernel function of the multi-kernel learning method， so as to enhance the representation ability of the multi-kernel learning method. Then， a generalization error bound with a convergence rate of O\left(\mathrm{1}/n\right) was proved based on the measure of principal eigenvalue ratio. On this basis， a new multi-kernel learning algorithm was designed in combination with the kernel alignment measure. Finally， experiments were carried out on several datasets. Experimental results show that compared with classification algorithms such as Adaboost and K-Nearest Neighbor （KNN）， the newly proposed multi-kernel learning algorithm has higher accuracy and better representation ability， which also verifies the feasibility and effectiveness of the proposed method.