This is an entry-level question for multiway matrix decompositions. I have a set/population $k$ of entities (here biological cells) for each of which I also have a number ($l$) of flavours of length $N$ vectors (genetic-like measurements for which $N \gg k$) which characterise them. Now if I take just one type of vector, and look at its values across all of the entities (cells), I do a PCA since I effectively have a $k \times N$ (depending on convention) array which I can explore in the conventional. If I repeat this analysis $l$ times for each flavour of the vector, I get $l$ very similar analyses but I would like to take an overall view. My question is this:
is it possible (or reasonable) to approach this as a multiway analysis on an $l \times k \times N$ data source says using a Tucker factorisation/tensor decomposition?
is this the most appropriate approach?
are there any available resources, papers or books that I should read to understand this?
The aim is to understand how the different vector flavours (types of genetic-like information) differ in the characterisation of the cells.
I'm currently working with the
rTensor package in R which I think may be based upon a similar one in MATLAB. I have a maths background and am in principle not afraid of tensors although this would be the first time I have used them for data analysis.