[MRG] Remove preprocessing the data for RCA

[wdevazelhes]

Fixes #125

This PR removes the preprocessing of the data in the algorithms.

TODO:

• when the uniformized init is merged [MRG] Uniformize initialization for all algorithms #195, ensure that the ChangedBehaviorMessage explains that in some cases 'pca' init is not used as before, and in order to use it one should set the 'init' parameter --> done in [MRG] Uniformize initialization for all algorithms #195
• add a small test to test the newly changed warning for RCA when the inner covariance matrix is singular

[wdevazelhes]

Note that this code was giving a PCA initialization at the same time, so for now we'll remove it, but I think I'll do the PR about initialization before merging this PR into master, and then we can merge it into this PR to keep the same possibility of initialization with PCA

[bellet]

There is still a warning that mentions pca_comps to update. if the matrix is low-rank (due to high dimension compared to the number of points) , we can suggest the user to use a dimensionality reduction technique such as PCA as preprocessing. Unless we have a better idea

[wdevazelhes]

I think this PR is ready to merge as soon as the initialization PR is merged (#195)

[wdevazelhes]

@bellet @perimosocordiae I guess this PR is ready to merge now

[bellet]

why is this centering step gone?

[wdevazelhes]

I guess because we should remove any pre-processing step, but I agree I didn't talk about it at all, maybe we should keep the ChangedBehaviorWarning message below, but rather replace "no longer trained on a preprocessed version" by "no longer trained on centered data by default", and encourage to use a "StandardScaler" if needed ?

[bellet]

Fair enough (I double-checked and this centering is not part of standard RCA)
Maybe keep ChangedBehaviorWarning but change to "no longer center the data before training RCA" (no need to mention scaler I think)
And in the deprecation warning, add the fact that PCA preprocessing should now be done by the user

Finally, have you checked the influence of removing the centering step on the examples?

[bellet]

Do we need a ChangedBehaviorWarning? The default behavior was pca_comps=None
Maybe the information in this warning should rather go to the deprecation warning?

[wdevazelhes]

see above

[bellet]

I think addressing #194 (comment) and then we can merge

[wdevazelhes]

I think addressing #194 (comment) and then we can merge

Done, I'll just check quickly what it changes on iris for instance, as you recommended for check-proof

[wdevazelhes]

With the same example as plot_metric_learning_examples.py, it seems that no centering does fine:

from metric_learn import RCA_Supervised
from sklearn.datasets import make_classification
from sklearn.manifold import TSNE
import matplotlib.pyplot as plt

X, y = make_classification(n_samples=100, n_classes=3, n_clusters_per_class=2,
                           n_informative=3, class_sep=4., n_features=5,
                           n_redundant=0, shuffle=True, random_state=42,
                           scale=[1, 1, 20, 20, 20])

tsne = TSNE()
X_e = tsne.fit_transform(X)
plt.figure()
plt.scatter(X_e[:, 0], X_e[:, 1], c=y)
plt.show()
rca = RCA_Supervised(num_chunks=30, chunk_size=2)
X_r = rca.fit_transform(X, y)
X_er = tsne.fit_transform(X_r)
plt.figure()
plt.scatter(X_er[:, 0], X_er[:, 1], c=y)
plt.show()

Here are the tsne plots after RCA transformation:

for this PR:

for master:

[wdevazelhes]

So I guess we're OK to merge now