基于概率判断函数的分类探讨——以玻璃分类为例  

Classification Problem Based on Probability Judgment Function--Taking Glass Classification as an Example

作　　者：姜永胜[1] 张俊芬 薛婷婷[1] 邢喜民 JIANG Yong-sheng;ZHANG Jun-fen;XUE Ting-ting;XING Xi-min(Xinjiang Institute of Engineering,Aidinghu Road,Urumqi 830023,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023

出　　处：《数学的实践与认识》2023年第10期116-125,共10页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区科技厅青年科学基金(2021D01B35);新疆维吾尔自治区高校科研计划自然科学基金(XJEDU2021Y048)。

摘　　要：分类问题在基因、化学、地质等领域都有着广泛的应用,在数据满足正态分布的前提下,利用一元正态分布函数的概率密度函数比值构造概率判断函数,建立数学模型,在默认阈值为α=0.5的前提下,对未知类型进行判断,并通过不同阈值下的正负谬误做误差估计,确定最优的阈值.以高钾类、铅钡类玻璃的风化、无风化四种数据为研究对象,利用概率判断函数对模型进行验证.结果表明,模型能准确的对待测的高钾类、铅钡类样本进行分类.在误差分析方面,通过改变阈值进行灵敏度分析,对于高钾类、铅钡类无风化问题,当阈值α=0.65时,误差最小.Classification problems are widely used in gene,chemistry,geology and so on.On the premise that the data satisfy the normal distribution,establishing a mathematical model through the probability judgment function using the ratio of the probability density function of the univariate normal distribution function.Under the premise that the default threshold is α=0.5,the unknown type is predicted,and the error estimation is made through the positive and negative errors under different thresholds to determine the optimal threshold.In this paper,the weathering and non weathering data of high potassium and lead barium glasses are taken as the research object,and the probability judgment function is used to predicted the unknown data.The results show that the model can accurately classify the samples of high potassium and lead barium.In terms of error analysis,sensitivity analysis is caculated by changing the threshold value.For the non weathering problem of high potassium and lead barium,when the threshold value isα=0.65,the error is the minimum.

关 键 词：正态分布 概率密度函数 概率判断函数 阈值 误差分析 

分 类 号：TQ171[化学工程—玻璃工业] O211.3[化学工程—硅酸盐工业]