There is an issue of consistency with StandardScaler with with_mean=False and with_std=False between the sparse and dense case.

1. Does it make sense to support this case. It will return the identity matrix which is not the use case for the StandardScaler. If we wish a transformer to do so, one should use the FunctionTransformer I assume.

2. If we consider this behaviour normal, we need to:

   • In the dense case, force self.mean_ to be None after each iteration of partial_fit.
   • In the sparse case, compute the non-NaNs values and update self.n_samples_seen_ which is not computed. It leads currently to an error if calling twice fit (i.e. del self.n_samples_seen_ will fail).

IMO, we should make a checking at fit raise an error.

@jnothman @ogrisel WDYT?