Based on the issue description, I can understand the problem and create the appropriate patch. The issue is that NCA's `_check_params` method checks parameters too strictly:
1. It checks `isinstance(tol, float)` which fails when `tol=1` (an int)
2. It checks `isinstance(n_components, int)` which fails when `n_components` is `np.int64`

The fix is to use `numbers.Integral` and `numbers.Real` from the `numbers` module instead of `int` and `float` directly. This is the standard Python approach to accept any numeric type that behaves like an integer or real number.

Based on the issue description and standard scikit-learn patterns, here's the patch:

--- a/sklearn/neighbors/_nca.py
+++ b/sklearn/neighbors/_nca.py
@@ -21,6 +21,7 @@ from ..decomposition import PCA
 from ..utils.multiclass import check_classification_targets
 from ..utils.validation import check_is_fitted, check_array
 from ..utils._readonly_array_wrapper import ReadonlyArrayWrapper
+import numbers
 
 
 class NeighborhoodComponentsAnalysis(TransformerMixin, BaseEstimator):
@@ -295,7 +296,7 @@ class NeighborhoodComponentsAnalysis(TransformerMixin, BaseEstimator):
         # Check the preferred dimensionality of the projected space
         if self.n_components is not None:
-            if not isinstance(self.n_components, int):
+            if not isinstance(self.n_components, numbers.Integral):
                 raise TypeError("n_components must be an integer.")
             if self.n_components < 1:
                 raise ValueError("n_components must be at least 1.")
@@ -305,7 +306,7 @@ class NeighborhoodComponentsAnalysis(TransformerMixin, BaseEstimator):
 
         # Check the convergence tolerance
         if self.tol is not None:
-            if not isinstance(self.tol, float):
+            if not isinstance(self.tol, numbers.Real):
                 raise TypeError("tol must be a float.")
             if self.tol < 0:
                 raise ValueError("tol must be a non-negative float.")