How can you do PCA on a matrix with vector-elements?

Question

I have a Matrix M x N x 2 and I want to apply PCA to it. I am aware, that normally you take just MxN matrices, but I am trying to do some work from this paper by Seiichi Uchida:

https://www.researchgate.net/publication/3973917_Using_eigen-deformations_in_handwritten_character_recognition (particularly 2.1 and 2.2)

The matrix is representing a deformation with the help of vectors. Each column is a vector(dimension = pixels) containing vectors(dimension = 2, representing coordinates)

Do I just have to concatenate the vectors, or how can I solve this?

Answer 1

I did not understand what you meant by concatenating the vectors.

Anyway, PCA is typically used to combine numerical continuous variables, so you can simply split the coordinates to two separate features and treat them independently as any other column.

Any option that turns the coordinates into non-numerical variables will perhaps cause the PCA to not being the best algorithm for feature reduction.