Functional Principal Component Analysis

[sebffischer]

besides the simple feature extraction through PipeOpFFS, another important method is functional PCA.

We can implement a PipeOpFPCA similar to PipeOpFFS that does a functional PCA.

I think the tfb_fpc function can be used here.

• [ ] Add PipeOp to overview in readme

[m-muecke]

https://tidyfun.github.io/tf/reference/tfb_fpc.html

[fabian-s]

s.th like this should do the trick:

library(tf)
x <- tf_rgp(10)
x_pc <- tfb_fpc(x, pve= .9) # truncate PC decomp at 90% explained variance

# PC score vectors for each function are simply the basis coefficient vectors
# making up the object 
# (without the first one, which is always 1 for the global mean function)
extract_score_matrix <- function(f) {
  assert_class(f, "tfb_fpc")
  f |> unclass() |> sapply(\(x) x[-1]) |> t()
}
extract_score_matrix(x_pc)