基于二元分割检测分段线性趋势中的多变点  

Multiple Change-points Detection in Piecewise Linear Trends Based on Binary Segmentation

作　　者：刘伟 胡尧 胡倩 LIU Wei;HU Yao;HU Qian(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China;Guizhou Provincial Key Laboratory of Public Big Data,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州省公共大数据重点实验室,贵阳550025

出　　处：《重庆工商大学学报（自然科学版）》2020年第6期32-38,共7页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11661018);贵州省科技计划项目(黔科合平台人才[2017]5788号).

摘　　要：变点检测问题一直是统计学中的热点研究之一,在实际的数据中,通常会在某一段具有线性增长或减少的趋势,这种趋势的起始点位置是未知的,因此针对此种具有分段线性趋势的一维数据,提出了一种多变点检测方法。该方法根据广义对数似然比所构造出的统计量,将二元分割方法、阈值准则和sSIC三者相结合,能快速有效地检测出数据中的多变点。数值模拟结果表明,对具有分段线性趋势的数据,检测变点的位置及数量很准确,检测结果令人满意。最后以深圳市北环大道新洲立交的车流量数据为例,分析出该区域在工作日和非工作日的变点分布特征,分析结果符合实际情况,可为交管部门的相关工作提供参考意见。Change point detection has always been one of the hot research topics in statistics.In actual data,there is usually a linear increase or decrease trend in a certain segment,the starting and ending point of this trend is unknown,thus,aiming at this kind of one-dimensional data with piecewise linear trend,a multiple change point detection method is proposed.Based on the statistics constructed by the generalized log-likelihood ratio,this method combines the binary segmentation method,threshold criterion,and Strengthened Schwarz information criterion to quickly and effectively detect multiple change points in the data.Numerical simulation results show that the method is very accurate in detecting the position and number of change points for the data with piecewise linear trends,and the detection results are satisfactory.Finally,by taking the traffic flow data of Xinzhou Interchange of North Ring Avenue in Shenzhen as an example,the distribution characteristics of the change point of the area on working days and non-working days are analyzed.The analysis results are consistent with the actual situation and can provide reference opinions for the relevant work of the traffic management departments.

关 键 词：多变点检测 sSIC 二元分割 线性趋势分段 

分 类 号：O212[理学—概率论与数理统计]