Severe bug in LDA (default algorithm)

The default algorithm in this package is wrong. We cannot use symmetric to evaluate the eigenvalue decomposition of

$Sw^-1 Sb$

, because that multiplication is not guaranteed symmetric.

We should always be using pinv. There should be no other option.

References:

• https://gitlab.idiap.ch/bob/bob.learn.linear/-/blob/master/bob/learn/linear/include/bob.learn.linear/lda.h#L49
• https://gitlab.idiap.ch/bob/bob.learn.linear/-/blob/master/bob/learn/linear/cpp/lda.cpp#L137

@sebastien.marcel, @amohammadi please take note of this (thanks to FSPR and bug tracking we could find this).

Just to keep track.

https://gitlab.idiap.ch/bob/antispoofing.utils/-/blob/master/antispoofing/utils/ml/lda.py#L12

https://gitlab.idiap.ch/bob/bob.bio.base/-/blob/master/bob/bio/base/algorithm/LDA.py#L60

on bob.learn.linear we use the wrong eigen decomposition if pinv=False

pinv=False for PAD too.

https://gitlab.idiap.ch/bob/bob.pad.base/-/blob/v2.3.1/bob/pad/base/algorithm/PadLDA.py#L36

I think it would be best to just replace this algorithm with scikit-learn.

mentioned in merge request !15 (closed)