The literature for PCA (acronym for Principal Component Analsys) consists mostly on dealing with quantitative variables which are preferably continuous. Koch gives a mathematical insight on why this is desirable on her book Analysis of Multivariate and High-Dimensional Data.
The goal of this project is to create a class of suitable transformations of ordinal data into continuous data such that PCA benefits from them being applied.
Categorical data will only be considered if the first goal turns out to be successful as the underlying space tends to be confusing.