[MRG] Fix mean centering in ot.dr.fda and ot.dr.wda - #840
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np.mean(X) returns the mean over all entries rather than the per-feature mean, so `X -= mx.reshape((1, -1))` subtracted a single scalar from every feature. The `proj` callables therefore did not center the data, contrary to their documented behaviour. In `fda` the same pattern appears in the class means, where `mxc[:, i] = np.mean(xc[i])` fills the column of class i with a scalar. Every class mean becomes a constant vector, so the between-class scatter matrix reduces to a multiple of the all-ones outer product and carries no information about which features separate the classes. The generalized eigenproblem eig(Cb, Cw + reg*I) then returns a direction driven only by the within-class scatter. On data separated along a single axis, `fda` returned a direction essentially orthogonal to it; it now agrees with sklearn's LinearDiscriminantAnalysis to within numerical precision. Both functions also mutated the caller's array through the in-place `-=`, which is now avoided. Adds non-regression tests for the recovered direction, for the centering of `proj`, and for the absence of input mutation.
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Types of changes
Bug fix (non-breaking change which fixes an issue).
Motivation and context / Related issue
np.mean(X)withoutaxisreturns a scalar;.reshape((1, -1))on it gives(1, 1)and broadcasts silently.X -= mx.reshape((1, -1))subtracts one scalar from every feature, soprojdoes not center as documented.wda's learnedPis unaffected — the cost sees only pairwise differences.fda,mxc[:, i] = np.mean(xc[i])makes every class mean a constant vector, soCb = [Σ_i (m_i − m̄)²]·11ᵀ: rank one, no information about which features separate the classes.Xin place.On 3 classes separated along feature 0 with 4 noise features,
fdagave[0.68, 0.99, 0.63, 1.00, 0.97]; now[1.00, 0.022, 0.043, 0.034, 0.124], matching sklearn's LDA to|cos| = 1.0.ot.dr.fdais the baseline inexamples/others/plot_WDA.py.How has this been tested (if it applies)
3 new tests, each verified failing on master.
test_dr.py9 passed, pre-commit clean.PR checklist