Singular Value Decomposition on Correspondence Analysis as Derivation of Principal Component Analysis

By dividing a data set into new sets of variables known as principal components, or PCs, Principal Component Analysis (PCA) is a popular method for lowering the dimensions of a data set while preserving as much variance as possible in the observed data set. The first few variables in the set maintain the majority of the variation found in the original variable since these principal components are sorted and uncorrelated. The number of variables in a multivariate analysis should always exceed the number of observations; nevertheless, this is not always true. Using Singular Value Decomposition (SVD) is more efficient when there are more variables than observations. Here, the theoretical study of SVD as a derivative of PCA was explored and adapted to analyze the discrete data, which is called Correspondence Analysis (CA). The application of this method in the analysis of ITB alumni tracer study data in study programs at the Faculty of Mathematics and Natural Sciences (FMIPA), School of Life Sciences and Technology (SITH) and School of Pharmacy (SF) for the location of residence provided some quite interesting conclusions. The trend of site selection based on the characteristics of the knowledge studied was presented in a graphical design through CA using SVD and PCA. CA gave two-dimensional plots for data classified according to the contingency table by biplot. Through the biplot, the row category for Mathematics study programs of FMIPA having an essential contribution to the positive pole of the PC first dimension was obtained, while the categories for Clinical and Community Pharmacy study programs of SF significantly contributed to the negative pole.