For the past few hours I've been trying to search what this linear assumption is. Some of the articles states that that your independent variables have to be linear in relationship and need some type of transformation if there is no linearity. Other articles state that your data has to be linearly separable. Which is it? Is it both?
Does it mean that that you first have to check if the independent variables are linear in relationship, then after applying PCA, check if the data is linearly separable?
Check if the data, before applying PCA, is linearly separable with techniques like linear programming.
Then there is KERNEL PCA which after searching states that it is an extension of PCA where it is applied to nonlinear data. Does that mean nonlinear in relationship or linear inseparable?