Data understanding with PCA: Structural and Variance Information plots

Principal Components Analysis (PCA) is a useful tool for discovering the relationships among the variables in a data set. Nonetheless, interpretation of a PCA model may be tricky, since loadings of high magnitude in a Principal Component (PC) do not necessarily imply correlation among the corresponding variables. To avoid misinterpretation of PCA, a new type of plots, named Structural and Variance Information (SVI) plots, is proposed. These plots are supported by a sound theoretical study of the variables relationships supplied by PCA, and provide the keys to understand these relationships. SVI plots are aimed at data understanding with PCA and are useful tools to determine the number of PCs in the model according to the pursued goal (e.g. data understanding, missing data recovery, data compression, multivariate statistical process control). Several simulated and real data set are used for illustration.