The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The metho...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
Based on the surveying data of strata-moving angle and the ordinary least squares regression,this paper is to construct,a regression model is constructed which is strata-moving parameterβconcerning the coal bed obliq...Based on the surveying data of strata-moving angle and the ordinary least squares regression,this paper is to construct,a regression model is constructed which is strata-moving parameterβconcerning the coal bed obliquity,coal thickness,mining depth,etc.But the regression is unsuccessful.The result is that none of the parameters is suited,this is not up to objective reality.This paper presents a novel method,partial least squares regression(PLS regression),to construct the statistic model of strata-moving parameterβ.The experiment shows that the forecasting model is reasonable.展开更多
基金Project(40144018)supported by the National Natural Science Foundation of China
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
基金Project(030501801)supported by the Key Laboratory of the State Bureau of Surveying and Mapping in Geographical Space InformationEngineering
文摘Based on the surveying data of strata-moving angle and the ordinary least squares regression,this paper is to construct,a regression model is constructed which is strata-moving parameterβconcerning the coal bed obliquity,coal thickness,mining depth,etc.But the regression is unsuccessful.The result is that none of the parameters is suited,this is not up to objective reality.This paper presents a novel method,partial least squares regression(PLS regression),to construct the statistic model of strata-moving parameterβ.The experiment shows that the forecasting model is reasonable.
