Tolerance in KMeans is with respect to the norm of the difference of centers.

[vnmabus]

The parameter tol is referred in the documentation as tolerance with respect to inertia:

scikit-learn/sklearn/cluster/_kmeans.py

Line 685 in b194674

Relative tolerance with regards to inertia to declare convergence.

However the tolerance was never measured against the difference in inertia, but as against the Frobenius norm of the difference in the cluster centers.

scikit-learn/sklearn/cluster/_kmeans.py

Lines 442 to 443 in b194674

	center_shift_total = squared_norm(centers_old - centers)
	if center_shift_total <= tol:

Either the documentation is wrong here or the check for convergence is wrong.

[madhuracj]

It looks more like the documentation is wrong.

[jeremiedbb]

Right, the documentation is wrong. Would you like to submit a PR ?

[madhuracj]

Sure, will do.