空间点所属空间体的距离判别法分析

Spatial entity determination of spatial points based on distance discriminant analysis

针对空间直角坐标系下空间点所属空间体的判定问题,该文提出一种采用距离判别法进行分析研究的方法。基于空间点的特点以及距离判别法的基本原理,通过建立一种以空间点的x、y、z坐标为判别因子,以马氏距离为判别距离的空间点所属性距离判别分析模型来完成对该问题的判定,并采用训练样本回代法和总体均值向量假设检验来验正该模型。通过40个训练样本的回代结果和两总体均值向量假设检验结果,证明了该方法的合理性和有效性。运用该模型,对4个待判样本进行判别,判别结果与真实情况一致,同时也证明了该方法的可行性。

In view of the determination problem that which spatial entity the spatial points belong to in the space rectangular coordinate system,this paper presented an analysis and research method through distance discriminant analysis.Based on the characteristics of spatial points and basic principle of distance discrimination analysis,a distance discriminant analysis model for the attributes of spatial points could be established to solve the mentioned question.This model used the x,y,zcoordinates of spatial points as the discrimination factors and used the Mahalanobis distance as the discrimination distance.The back substitution method for training samples and hypothesis testing method for overall mean vectors were used to test the model.The results of back substitution method of 40 training samples and hypothesis testing method of two overall mean vectors proved the rationality and validity of the method.Due to the consistency of the discriminant results of 4pending samples using this method and the real situation,the feasibility of the method also be proved.