I think there are a few hints in the prequel trilogy that Yoda had a surprisingly emotional attachment to Padme. When Yoda sees Padme in Palpatine's office, in AOTC, he expresses his relief that she is alive. He could be expected to do as much, but the way the lines are spoken and the face is animated, he seems particularly sincere and earnest. He could be expected to know about what happened, but he talks to Padme like a person he knows, not just a Senator among hundreds that he knows about. All this evidence is pretty circumstantial, but the scene connects in my mind to another, less equivocal scene in ROTS, when Padme dies. Yoda looks really upset. Again, maybe that's to be expected, but why does he look as upset about Padme's death as he does about the death of the Jedi Order, and why does Lucas choose to show Yoda grieving right after Padme dies? The (possible) implication seems to be that Yoda is having a particularly strong emotional response. So is Yoda just naturally empathetic to everyone, or is a personal relationship with Padme one of the many he has cultivated in eight hundred years of interaction with the people of the Republic (I'm surprised his friendship with Chewbacca never came up with Luke on some rainy Dagobah day when they were stuck indoors or something)? Perhaps Yoda had some unshown dealings or negotiations with Padme on Naboo at the end of TPM, when he visits that planet.