On The Mathematical Model And Application Of Stepwise Correspondence Analysis

Correspondence analysis is a multivariate statistical analysis method developed on the basis of R-factor analysis and Q-factor analysis.It's a new multivariate statixtical analysis technique developed in recent years.We can constituted by the qualitative variables by analyzing the interaction matrix to reveal the conections between the variables.Revealed that the same vatiables can be the difference between the various categories, and different variables corresponding relationship between each category. Departure from the original data matrix I=tr(T),and T is the covariance matix of two properties'relevance. And then calculate the correlation matrix eigenvalues and eigenvectors of the sample scores and variable rates.Stepwise Correspondence Analysis is based on the correspondence analysis, in the new perspective, though variable selection and sample selection to optimize the correspondence analysis of the mathematical model. Under some metics, vatiables can be drawn with fewer variables to characterize the original portrait of the relationship between the various samples. Discard unimportant variables, leaving the more important variables.By using mathematical software, followed by removal of variable loop, then compare the D(V,Vl), remove the variable which correspond to the smallest D(V,Vl),until the results we require.In which,After giving the mathematical model, this paper applied the methods and ideas of the model to actual productions. And improce the correspondence analysis model to draw some basic results. Though the comparison and by using the"proc corresp"program of the statistical software we can abtain the results as follows: summary statistics of sample points, sample point coordinates which can denote the coordinates and help us classify the samples according to the coordinates of each sample, the principal inertia and chi-square value,indices of the coordinates which contribute most to inertia of the sample points,partial contributions to inertia for the sample points,squared cosines for each sample point, summary statistics for the column points and the different sample points of comparison results. We make a detailed analysis on the actual operation of the example results. Stepwise Correspondence Analysis so as to arrive at some aspects of the application is quite practical and has a certain superiority.The first chapter introduces the basic mathematical model of correspondence analysis.The second chapter is described the basic principle of Stepwise Correspondence Analysis.The third chapter introduces the theoretical steps of Stepwise Correspondence Analysis.Chapter IV is about the Correspondence Analysis and Stepwise Correspondence Analysis examples of the methods used.Chapter V summarizes the examples of Stepwise Correspondence Analysis and analyzes some results, and compared with the Correspondence Analysis.