> for me the semantic is normalize = make columns unit norm
>
> But this is not the case here either: here it centers by column and scale by the column standard deviation to make each non-zero column scaled to unit variance.

AFAIK Ridge uses center_data in linear_model.base so it devides features by:

X_std = np.sqrt(np.sum(X ** 2, axis=0))

which is not a really an std dev (no div by n_samples).

indeed the scaling is applied before centering if required by fit_intercept

> Feature-wise centering + unit variance scaling is often referred to as "standardization": http://en.wikipedia.org/wiki/Standardizing .

we use unit norm with X_std = np.sqrt(np.sum(X ** 2, axis=0))

> That being said I am ok with leaving the normalize keyword of linear regression models as it is. For the non-linear ridge classifier though, I don't know what to expect. Should the non-linear ridge model do the "normalization" in the kernel space instead?

yes in kernel space if it's precomputed at some point.