Research And Application Of Kernel Logistic Regression Algorithm

As a classical linear classification algorithm,the limitation of logical regression is that it can not work on non-linear data sets.At present,the common method is to combine logistic regression algorithms with kernel trick to map non-linear data to a high-dimensional space,making it structured and linearly separable in this high-dimensional space.However,with the increasing of data scale,the use of kernel trick is more and more limited.In the case of large-scale data,the storage and calculation of the kernel matrix are very expensive.How to solve the cost problem of the kernel matrix and how to optimize the process of classification algorithm and improve the classification accuracy are the current urgent problems.In addition,in order to apply the algorithm in practice,this thesis designs and implements a remote sensing image classification system,and successfully applies the research results of the kernel logistic regression algorithm to remote sensing image classification.The main research contents and contributions of this thesis are as follows:1.The research of the low-rank approximate kernel logic regression algorithm.For the problem that the kernel trick introduces a kernel matrix which is positively correlated with the data scale,thus increasing the time cost of the algorithm.This thesis introduces a low-rank approximation method to approximate the kernel matrix,which not only speeds up the kernel matrix but also removes redundant information from the data to improve classification accuracy.At the same time,a fast dual optimization algorithm is used to optimize the solution,which prevents the kernel matrix from participating in the iterative operation,further reducing the algorithm's time overhead.2.The research of the multi-kernel sparse multinomial logistic regression algorithm.First,considering that the kernel logistic regression algorithm is generally applicable to the problem of binary classification,it is extended to a kernel sparse multinomial logistic regression algorithm suitable for multi-class tasks and made it suitable for sparse feature data sets.However,because the kernel function of single-kernel learning is single,the data cannot be fully expressed,and in order to make the choice of kernel functions more flexible,multi-kernel learning is introduced.Linearly combine multiple kernel functions of different types or different parameters.Finally,the sparse optimization algorithm is used to optimize the multi-kernel sparse multinomial logistic regression.3.Based on the research of the kernel logistic regression algorithm,this thesis solves the problem that heterogeneous and nonlinear features in remote sensing images make it difficult to classify.Finally,the kernel logistic regression algorithm is applied to the remote sensing image classification task with practical engineering significance,and a remote sensing image classification simulation system is designed.