FPCA on FDataIrregular about scikit-fda

[eliegoudout]

I am personally not familiar enough wit this pacage to answer your question, sorry. Someone else might!

[ooodragon94]

Looking that the source code, it seems like _weights variable seems to play important role in cholesky decomposition (error described above).
When not given, fPCA will initialize it to list of zeros with length of a function. I simply put ones instead of zeros when initializing FPCA.
Seems like it is working as expected, since increasing q (=components to keep in PCA) gives smaller error.

q = 5
function_len = train_data[0].data_matrix.squeeze().shape
fpca_clean = FPCA(n_components=q, _weights=np.ones(function_len))
fpca_clean.fit(train_data)

[eliegoudout]

I believe that at the moment, even for FDataGrid, the package doesn't provide out of the box FPCA for $\mathbb{R}^n\rightarrow\mathbb{R}$ when $n\geqslant 2$. For further information and a potential workaround, I'd point towards #512.

[ooodragon94]

@eliegoudout
thank you for your reply.
That's a bad news.... :(
Could any other libraries work? (ex. https://fdasrsf-python.readthedocs.io/en/latest/fPCA.html)
At least if it works for regular grid, I think I can process the data with interpolation

[ooodragon94]

As eliegoudout referenced, I'm trying out a method explained in #512 where I can do fPCA with single dimension function (R -> R) and then add up all errors on other dimensions.

However, I'm facing an error "numpy.linalg.LinAlgError: Matrix is not positive definite" when doing
q = 2
fpca_clean = FPCA(n_components=q)
fpca_clean.fit(fd)

it seems like an error while doing inverse transform for PCA. When does it work and when does it not work?