kernel_approximation.Nystroem with precomputed kernel

Describe the bug

I am trying to get a Nystroem approximation of a pre computed kernel but it throws an error if I use n_components anything less than the number of datapoints. Unless my understanding is wrong, does this not defeat the point of the approximation? Please advise, code below:

I have come from this resolved issue https://github.com/scikit-learn/scikit-learn/issues/14641

Steps/Code to Reproduce

from sklearn.svm import SVC
from sklearn.kernel_approximation import Nystroem
 
# data shape (3000,50)
# kernel matrix shape (3000,3000)
clf = SVC()
feature_map_nystroem = Nystroem(
    kernel = 'precomputed',
    random_state=1,
    n_components=300
)
kernel_transformed = feature_map_nystroem.fit_transform(kernel)
clf.fit(kernel_transformed, y)

Expected Results

I expect this to work.

Actual Results

Instead it gives error:

in check_pairwise_arrays(X, Y, precomputed, dtype, accept_sparse, force_all_finite, copy)
    153 if precomputed:
    154     if X.shape[1] != Y.shape[0]:
--> 155 raise ValueError("Precomputed metric requires shape "

    156                 "(n_queries, n_indexed). Got (%d, %d) "
    157                          "for %d indexed." %
    158                          (X.shape[0], X.shape[1], Y.shape[0]))
    159 elif X.shape[1] != Y.shape[1]:
    160     raise ValueError("Incompatible dimension for X and Y matrices: "
    161                      "X.shape[1] == %d while Y.shape[1] == %d" % (
    162                          X.shape[1], Y.shape[1]))
 
ValueError: Precomputed metric requires shape (n_queries, n_indexed). Got (300, 3000) for 300 indexed.

Versions

System:
    python: 3.8.19 (default, Mar 20 2024, 19:58:24)  [GCC 11.2.0]
executable: /opt/conda/miniconda3/envs/python3.8/bin/python
   machine: Linux-6.1.0-21-cloud-amd64-x86_64-with-glibc2.17
 
Python dependencies:
          pip: 24.0
   setuptools: 63.1.0
      sklearn: 0.24.2
        numpy: 1.21.6
        scipy: 1.10.1
       Cython: 3.0.10
       pandas: 1.2.5
   matplotlib: 3.4.3
       joblib: 1.4.2
threadpoolctl: 3.5.0

Start with sklearn.kernel_approximation.Nystroem and trace its precomputed-kernel path into check_pairwise_arrays. Reproduce the provided 3000-by-3000 kernel example with n_components=300, then verify that the precomputed case supports the expected approximation shape without the shown validation error.