| Multi-kernel learning is a popular and important kernel method,which is widely used in various fields.However,the basic kernel function structure adopted by most multi-kernel learning methods is too simple,and the representation ability is insufficient when dealing with problems such as large-scale data and uneven distribution.After the base kernel function is determined,in the multi-kernel learning method,the base kernel weight calculation will also have a great impact on its performance.The traditional method of calculating the weight of the base kernel usually only measures the expressive ability of the base kernel function in the sample data,and the consideration is too simple.In addition,kernel matrices are computationally expensive in large-scale datasets,which makes multi-kernel learning difficult to be applied to large-scale problem solving.Based on the problems described above,the research work of this paper is mainly to improve the performance and operating efficiency of multi-core learning algorithms on large-scale data sets.The work content is mainly reflected in the following aspects:(1)A neural tangent kernel-based multi-kernel learning algorithm NTK-MKL is proposed.Through theoretical and experimental research on finite-width and infinite-width neural tangent kernels,it is proved that it has better performance than traditional basis kernel functions.Then,the neural tangent kernel is used to replace the traditional base kernel function(such as polynomial kernel,Gaussian kernel and linear kernel,etc.)as the base kernel function of multi-kernel learning,so as to improve the representation ability of multi-kernel learning method.(2)Propose a multi-kernel learning algorithm PK-MKL based on principal eigenvalue ratio and kernel target alignment.The algorithm calculates the main feature ratio value of NTK and the kernel target alignment value,and then combines the two to form a new metric,and then uses the calculated metric value as the weight of the NTK kernel for multi-kernel combination.The algorithm considers both the representation ability of the base kernel function on the sample data and the complexity of the base kernel function,which can effectively improve the performance of multi-kernel learning.(3)A multi-kernel learning algorithm NS-MKL based on NTKSketch is proposed.The algorithm obtains the explicit NTK feature map by using the tensor product of the arccosine kernel feature map;and then obtains the random feature of NTK by sampling the feature space of the arccosine kernel,reducing the number of NTK features.Next,the Tensor Sketch algorithm is used to approximate the tensor product of the features generated in successive layers,reducing the dimensionality of the features and thus speeding up the operational efficiency of the multi-kernel learning algorithm.In addition,the NS-MKL algorithm is applied to the problem of oil well fracturing oil stimulation effect prediction to verify the effectiveness and feasibility of the algorithm. |
