基于高斯混合模型

摘要中小学作为城市最重要的公共设施之一，目前还没有统一的规划标准。我国目前的中小学用地规划是根据各地区政府的相关规定和学校周围实际情况进行的。在城市化进程中，随着新城建设和旧城改造，中小学设施方面的问题逐渐显现，如教师流失、择校过多、学位不足、个别学校规模过大、学校服务半径存在盲点、学校所在街区高峰期交通拥堵等。传统的中小学选址方法是以服务半径作为选址的指标，然而，这并没有考虑到，由于交通、建筑和学校通勤期间的道路状况和学生的分布等因素，到学校的实际距离与服务半径不能很好地耦合。本文在广泛查阅文献的基础上对目前国内外关于高斯混合模型聚类、半监督聚类以及基于高斯混合模型的半监督聚类的研究现状进行了较为深入的研究。通过比较它的研究内容和方法，并将其与本工作的目标联系起来，在一个新的视角提出了以高斯混合模型作为基础的半监督聚类算法CGMM(Constrained GaussianMixture Model)。该算法引入数据类标签和成对约束两种监督信息作为先验知识来协助指导聚类过程，基本思想是根据样本实例属于混合高斯成分的概率y和成对约束的组合来分配数据点。在算法研究的基础上，本文将提出的CGMM算法与传统的无监督高斯混合GMM聚类算法相比，并将最后结果的误差性作为实验结果的评价标准。对算法的结果进行了检验，并确定了该算法的可行性和有效性。然后以该算法为基础，设计与实现了基于CGMM算法的培训学校选址与排课系统。关键词：高斯混合聚类；学校选址：学生排课Research and implementation of school location and student coursescheduling system based on Gaussian mixture clustering algorithmAbstractAs one of the most important urban public supporting facilities,the relevant planningstandards of primary and secondary schools do not have unified normative implementationguidelines.The current location planning of primary and secondary schools in China is basicallybased on the calculation of various indicators according to the actual situation under theframework of the national standard.With the development of urbanization and the promotion ofnew town construction and old city renewal,the problems existing in the allocation of primary andsecondary schools are gradually exposed,such as the waste of teachers'resources,excessiveschool selection,insufficient degrees,too large scale of a single school,blind spots in the schoolservice radius,road traffic congestion during the peak period of school attendance and schoolingin the block,which are common problems caused by improper location of primary and secondaryschools.The traditional location planning method of primary and secondary schools mainly takesthe service radius as the location evaluation index,but it does not take into account thephenomenon that the actual school distance and service radius can not be well coupled due to theactual conditions of transportation,buildings,streets and so on.Firstly,this paper summarizes the research status of Gaussian mixture model clustering,semisupervised clustering and semi supervised clustering based on Gaussian mixture model inacademic circles at home and abroad.Then,by comparing the previous research contents andmethods of scholars,and combined with the research task of this paper,a semi supervisedclustering algorithm CGMM (constrained Gaussian mixture model)based on Gaussian mixturemodel is proposed from a new perspective.Based on the idea of Gaussian prior information,thealgorithm introduces two kinds of prior information to assist the clustering process y And pairwiseconstraints to allocate data points.Finally,the CGMM algorithm proposed in this paper iscompared with the traditional unsupervised simultaneous interpreting algorithm of Gauss mixturemodel GMM (Gaussian Mixture Model),semi supervised leaming algorithm Boostcluster(Boosting Clustering)and supervised classification algorithm LR (Logistic