THE EFFECT OF SINGULAR VALUE DECOMPOSITION ON CORRESPONDENCE ANALYSIS MAPS (CASE STUDY: SIGMA PHASE DATA ON STAINLESS STEEL)

• Main Author: Dominicus, Daniel
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/84064
• Institution: Institut Teknologi Bandung

Correspondence Analysis (CA) is a method for analyzing qualitative categorical data that represents the dependency between two categorical variables, rows, and columns, and then visualizes them on a correspondence map. The coordinates of the row and column categories on the map and the map's quality are influenced by the eigenvalues (????) from the singular value decomposition (SVD) process. This final project focuses on the role of eigenvalues ????1 and ????2 from a 3×5 contingency table on the correspondence map and the elliptical confidence regions to assess the stability and significance of row and column variables. Additionally, a goodness-of-fit test will be conducted between the original data and the estimated data from observers by providing proportional distributions to the total rows and reviewing the conformity of these distributions with the CA of the original data. The CA process begins by forming a contingency table in proportions, calculating the marginal row and column probability mass functions (pmf), and the standardization matrix S. SVD is performed on the asymmetric matrix S, which is decomposed into matrices U, D, and ????????, which are used to form row coordinates (F) and column coordinates (G) and build the semi-major and semi-minor axes for the elliptical confidence regions. The CA process is applied to the data of sigma phase (????), which is the phase that affects the increase of corrosion risk of stainless steel (SS) with the row variable being rust location Bar={A, B, C} and the column variable being rust color level Kol={1,2,3,4,5}. Based on the CA results, the relationship between row variable categories and column variable categories will be obtained based on the proximity of the coordinates representing these categories, and the area of the confidence regions for each category will be reviewed. Additionally, In addition, the effect of the distribution given to the original data on the change of the ???? phase effect will also be examined by comparing the CA results of the estimated data with the original data.