Aiming at the problem that the clustering results of K-Means clustering algorithm are affected by the sample distribution because of using the mean to update the cluster centers， a Neural Tangent Kernel K-Means （NTKKM） clustering algorithm was proposed. Firstly， the data of the input space were mapped to the high-dimensional feature space through the Neural Tangent Kernel （NTK）， then the K-Means clustering was performed in the high-dimensional feature space， and the cluster centers were updated by taking into account the distance between clusters and within clusters at the same time. Finally， the clustering results were obtained. On the car and breast-tissue datasets， three evaluation indexes including accuracy， Adjusted Rand Index （ARI） and FM index of NTKKM clustering algorithm and comparison algorithms were counted. Experimental results show that the effect of clustering and the stability of NTKKM clustering algorithm are better than those of K-Means clustering algorithm and Gaussian kernel K?Means clustering algorithm. Compared with the traditional K?Means clustering algorithm， NTKKM clustering algorithm has the accuracy increased by 14.9% and 9.4% respectively， the ARI increased by 9.7% and 18.0% respectively， and the FM index increased by 12.0% and 12.0% respectively， indicating the excellent clustering performance of NTKKM clustering algorithm.

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.