Research And Application Of Projection Pursuit Model

Projection pursuit is an exploratory analysis method.By projecting high-dimensional data into low dimensional space,we can search for the projection of the original high dimensional data structure or feature,so as to achieve the purpose of studying and analyzing high-dimensional data.Projection pursuit method provides a new theoretical method for the analysis of high dimensional data with non-normal nonlinearity.Since it was proposed,it has been paid close attention to by many scholars at home and abroad.Therefore,this paper studies the projection pursuit model.In this paper,the basic ideas and research work of projection pursuit are summarized,and the selection and construction of projection index function are discussed.In this paper,three kinds of projection pursuit models are proposed and applied to the comprehensive evaluation and prediction of high dimensional practical problems.The research work of this paper is summarized as follows.In this paper,the particle swarm optimization(PSO)algorithm is introduced to avoid the problem that the traditional projection direction optimization method is easy to fall into local optimum or premature convergence.In this paper,a cooperative mechanism is introduced to improve the particle swarm optimization algorithm.The improved particle swarm optimization algorithm can improve the accuracy and convergence speed of the model when solving the multi parameter optimization problem.In the classification and comprehensive evaluation of multiple factors,the traditional methods have the problems of poor objectivity of index weight assignment and low accuracy of evaluation results.To solve this problem,two kinds of projection pursuit cluster analysis models are proposed according to the structural characteristics and evaluation criteria.The two kinds of projection pursuit cluster analysis models are projection pursuit classification model and projection pursuit interpolation model.In order to establish the projection pursuit classification model based on particle swarm optimization,we choose the product of one dimension scatter and local density as the projection index function to highlight the evaluation sample,and using particle swarm algorithm to optimize the projection index function.The projection pursuit interpolation model is established to describe the relationship between the projection value and the grade of evaluation criteria.These two kinds of models avoid the artificial interference of expert weighting,and classify and evaluate the influence of multiple factors completely according to the characteristics of sample data.The two models were applied to the evaluation of rice irrigation system and the evaluation of soil quality.The result of the evaluation is scientific and reasonable,which verifies the accuracy and feasibility of the two kinds of projection pursuit cluster analysis model.In order to solve the problem of multivariate nonlinear prediction,this paper constructs a projection pursuit regression model based on Hermite polynomials.The model is a combination of regression analysis and projection pursuit,and the Hermite polynomial is used to fit the one-dimensional ridge function of the model.Cooperative particle swarm optimization algorithm is used to optimize the projection direction and polynomial coefficients in parallel.The model is applied to the annual runoff prediction,and the prediction results verify the feasibility of the model.At the same time,compared with the basic particle swarm optimization algorithm and the real coded genetic algorithm,the results show that the cooperative particle swarm optimization algorithm has better convergence in the multi parameter optimization problem.This paper will construct a coupling model of projection pursuit neural network based on the combination of neural network and projection regression model.The coupling model avoids the disadvantages of the projection pursuit regression model in the multivariate nonlinear prediction,which is too dependent on the data sample and weak fault tolerance.Similarly,the cooperative particle swarm optimization algorithm is used to optimize the projection direction,the neuron function and the threshold value.The coupling model and projection pursuit regression model were used to predict the water resources carrying capacity.The results show that the self-learning and adaptability of projection pursuit coupling model based on neural network.