Determine components for PCACompressionOp automatically

[ckolbPTB]

          Maybe we want to add the option to determine n_components automatically from the data? For an old project I implemented this using one approach and looked up two other ones, that I didn't implement yet. Not sure if we want this option (n_components could then maybe be of type int or Literal(implemented methods)), but I will paste my old code/references here just in case:

def det_malinowski_factor(eigenvalues: np.ndarray) -> int:
    """
    Determines minimum number of principal components according to: Malinowski, E. R. Determination of the number of
    factors and the experimental error in a data matrix. Anal. Chem. 49, 612–617 (1977).
    """
    ind = np.zeros([eigenvalues.shape[0]-1, 1])
    for n in range(ind.shape[0]):
        ind[n] = np.sqrt(np.sum(eigenvalues[n:]/(eigenvalues.shape[0]-(n+1)))) / (eigenvalues.shape[0]-(n+1))**2

    return int(np.argmin(ind))


def det_nelson_factor(eigenvalues: np.ndarray) -> int:
    """
    Determines minimum number of principal components according to: Nelson, L.R. (2005). Some observations on the
    scree test, and on coefficient alpha. Thai Journal of Educational Research and Measurement: 3(1), 1-17.
    """
    # Todo: implement function :)
    pass


def det_median_noise_factor(eigenvalues: np.ndarray) -> int:
    """
    Determines minimum number of principal components according to: Manjón, J.V. et al. (2015). MRI noise estimation and
    denoising using non-local PCA. Medical Image Analysis 22 (2015) 35–47
    """
    # Todo: implement function :)
    pass

Originally posted by @schuenke in #181 (comment)