Application Of Random Forests Kernel Function In Regression And Classification Problems With Spherical Data

Spherical data,as the data describing the direction,is a type of data that exists widely in nature.However,in some practical studies,the coexistence of spherical data and linear data in Euclidean space will be encountered.For example,when analyzing wind energy,the predictors include wind direction,wind speed,and time.At present,there are few related studies on statistical models of mixed data.The research topic of thesis is regression and classification with spherical predictors,focusing on the fitting ability of nonparametric regression models based on random forests kernels on spherical data.The content is divided into: 1.Applying the random forests algorithm as an adaptive kernel functions to nonparametric regression.For the regression problem of spherical predictors and mixed predictors,we propose a local linear regression model based on random forests kernel.Then we briefly discuss the asymptotic properties of random forests kernel estimation by simulation experiments.2.Extending nonparametric estimation methods to binary classification problems with spherical predictors.The local maximum likelihood estimation of the logistic regression function is performed to establish a local linear logistic regression model based on the random forests kernel.Simulation and real experiments of regression and classification show that compared with von Mises-Fisher（v MF）kernel,Gaussian kernel and Gaussian-spherical kernel,random forests kernel has more outstanding performance in fitting power and computational efficiency.In terms of fitting power,v MF kernel and Gaussian-spherical kernel only perform well in low-dimensional data,and perform poorly in high-dimensional data.For the random forests kernel,its fitting error in low dimensions is very close to that of the v MF kernel and the Gaussian-spherical kernel.In the high-dimensional case,the random forests kernel shows good performance,its fitting effect is better than the other three kernel functions.In terms of computational efficiency,the random forests kernel does not require bandwidth selection or any parameter estimation,the calculation speed is several times to dozens of times that of the other three kernel functions.In the classification model,we compare the nonparametric binary classification model based on random forest kernel with classifiers such as random forest and support vector machine.Results show that our model outperforms several other classifiers in low-and medium-dimensional,and approaches random forests in high dimensions.