THE ROLE OF QR ALGORITHM IN CORRESPONDENCE ANALYSIS (CASE STUDY: CIGARETTE ADVERTISEMENT DATA IN INDONESIA)

• Main Author: Annisa Riefina, Dana
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/50139
• Institution: Institut Teknologi Bandung

Correspondence analysis is a graphical multivariate analysis to reduce dimension of standardized residual matrix (????). Dimension reduction is done with singular value decomposition or eigenvalue decomposition od covariance matrix (?????) of ????. This matrix is real symmetric, positive semidefinite, and one of the eigenvalue is 0. In analytical method, eigenvalue is calculated by characteristic polynomial, but higher degree polynomials the solution can’t be calculated. Therefore, numerical method of finding eigenvalue is proposed, one of the method is using QR algorithm. Basic idea of QR algorithm is doing QR decomposition in iterative way. QR algorithm is modified to speed up convergency with Householder transformation and shifting constant. Householder transformation can obtain tridiagonal symmetric matrix which similar with ?????. For ?????????×????, ????=3,4,…,12 obtained that iteration of QR algorithm is 2-5 times larger than Shifting-QR algorithm. However the execution time is not significantly different, because in Shifting-QR algorithm needs an additional calculation for shifting constant. CA method is applied to Cigarette Advertisement Data in Indonesia with two categorical variable, cigarette company and television channel. There are 13 categories of cigarette company and 12 categories for television channel. With Phi-Cramer statistic, this data is satisfied the association test. Using QR algorithm to find the eigenvalues, two dimensional correspondence map is obtained with cumulative inertia 68.5%. From correspondence map, we can conclude characteristics of cigarette advertisement from categories intravariable and association of categories inter-variable.