Analysis And Application Of Density Estimation Based On Controllable Diffusion Method

Nowadays,many discrete data acquisition are presented with geotag information.The occurrence positions of discrete data can be represent by a two-dimensional geographic coordinates.Given discrete events data,it can produce a probability density map that can model the relative probability of events occurring in order to intuitively understand the size and the trends of such events within the region.Common methods do not take geographical information into account.The most commonly used method is the kernel density estimation does not use the prior knowledge of the data distribution and makes no assumptions,which belongs to one of the common methods of nonparametric test.The core idea of kernel density estimation method is characterized by simple thinking and it is a method of estimating its density from the data sample.But under the condition of discrete data which is dense,its computational complexity is too high.In recent years,the model of probability density estimation has been improving.Many of the methods evolved by maximum likelihood estimation are proposed.This method obtains the probability density estimate by solving the minimization program.A classic approach is to add penalty functions as a regular term for the minimization problem.The choice of penalty function corresponds to a different model which include total variation maximum penalty likelihood estimation method(TV-MPLE).The traditional method did not join the consideration of geographic information.In applications,these methods could result in the support of probability density appearing in the unrealistic geographical locations.For example,crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans,mountains,and so forth.In this thesis,a modified maximum penalty likelihood estimation method based on total variation is proposed.The model uses the geographic information to preferentially divide the region into an effective region and an invalid region,and the probability density remains at zero in the invalid region.It can both ensure the smoothness of the density estimation and ensure the density estimation of discrete events do not appear in the invalid location.This thesis also analyzes and compares the characteristics of two solving methods: the split Bergman method and the gradient projection descent method.This article verifies the superiority of the new algorithm by comparing the new algorithm with the traditional method through applying simulation discrete data.Then,this article applies this method on criminal density estimation of a city to verify the feasibility of solving actual issue and give police a guidance on deployment.Then,this thesis focuses on the effect of density estimation of each algorithm in the case of sparse discrete data and analyzing the reason why the density estimate is too smooth in the case of sparse data with MTV-MPLE.In this way,the model is extended and the division of the effective area is further subdivided.According to the nature of the discrete event itself,the effective region is divided into positive and negative regions.In the process of solving the diffusion equation by iteration,the Gaussian kernel density estimation is used to guide the diffusion.In the experimental test of this method,this thesis divide the effective and ineffective regions by decomposing the texture of the satellite image without any priori.Above all,this paper ultimately makes the estimation results more realistic in the case of sparsely populated data.