Principal Component Analysis Of Interval Symbol Data And Validity Study

With the emergence and popularity of computers,data has exploded.Faced with a variety of complex high-dimensional data,the selection of appropriate data analysis technology can effectively solve the dimensional disaster.The traditional data analysis teclhnology is only for point data,it is difficult to grasp the intrinsic properties of the data.The symbol data analysis technology is based on the idea of classification "Dackaaina",and can grasp the inherent relationship of data from the whole.This paper mainly conducts principa component analysis on interval-type symbol data,and deeply compares and analyzes is effectivenessFirstly,aiming at the defects of larae amount of calculation and inaccurate analvsis results of the existing interval-type symbol data Principal Component Analysis,two improved algorithms are proposed:1MO-PCA and ECM-PCA.IMO-PCA derives the definitions of the covariance matrix and the correlation coefficient matrix of the interval matrix according to the interval matrix algorithm.The interval eigenvector of the correlation coefficient matrix is obtained by the spectral radius method,and the interval principal component is obtained from the interval eigenvector;ECM-PCA Through the analog real variable,the empirical joint distribution function of the interval variable is obtained,and then the mean,variance.covariance and correlation coefficient of the interval variable are derived.The interval principal component is obtained from the correlation coefficient matrix.Both of'the above improved algorithms assume that the sample data is a normal distribution interval number,which is more in line with the distribution of real data.Then compare the effectiveness of the existing interval principal component anal,ysis method and the improved two algorithms.Aiming at the single defect of the traditional principal component validity index measurement method,two measurement factors affectino the validity index are proposed.The random simulation experiment is designed and implemented,and furtlier research is carried out with examples.The experimental results show that the two methods proposed in this paper have obvious advantages compared with the existing interval principal component analysis method,and tme analysis resuis,are more accurate and cao objectively reflect the reality.Finally,the algorithm proposeu in this,paper is applied.