diff --git a/src/skmatter/preprocessing/_data.py b/src/skmatter/preprocessing/_data.py
index 07160dea4..a805e7460 100644
--- a/src/skmatter/preprocessing/_data.py
+++ b/src/skmatter/preprocessing/_data.py
@@ -524,9 +524,15 @@ def fit(self, Knm, Kmm, y=None, sample_weight=None):
         if self.with_trace:
             Knm_centered = Knm - self.K_fit_rows_
 
-            Khat = Knm_centered @ np.linalg.pinv(Kmm, self.rcond) @ Knm_centered.T
+            # The following is more correctly written as Knm @ Kmm^{-1} @ Knm.T
+            # but has been changed to Knm.T @ Knm @ Kmm^{-1} to avoid the memory
+            # overload often caused by storing n x n matrices. This is fine
+            # for the following trace, but should not be used for other operations.
+            Khat_trace = np.trace(
+                Knm_centered.T @ Knm_centered @ np.linalg.pinv(Kmm, self.rcond)
+            )
 
-            self.scale_ = np.sqrt(np.trace(Khat) / Knm.shape[0])
+            self.scale_ = Khat_trace / Knm.shape[0]
         else:
             self.scale_ = 1.0