In current KernelPCA _fit_transform implementation, nothing prevents or alerts users that the eigenvalue decomposition presents some numerical or conditioning issue. We could check the following (thanks https://github.com/GabrielRilling for the suggestion!):

• significant imaginary parts in eigenvalues (raise ValueError)
• significant negative eigenvalues (throw KernelWarning if there is at least a positive eigenvalue, otherwise raise ValueError)
• significant conditioning issues (huge ratio > 1e12 between large and small eigenvalues) (throw KernelWarning)

We should also perform some cleaning for non-significant issues (due to numerical approximation) and for the above when no error is raised:

• remove unsignificant imaginary parts
• set negative eigenvalues to zero
• set extremely small eigenvalues (with respect to the largest ones) to zero

This will provide more robust and stable numerical computation across runs/platforms/noise.