It's also confirmed in the games themselves.
The cloaked figure says he "hid his research data inside the boy (Sora) while he slept" and that his mind clouded by revenge brought much suffering upon beings connected to Sora.
It's pretty easy to deduce that this is Ansem the Wise since it all also
fits together with how he acted in the last third of Kingdom Hearts 2.
He was pretty remorseful for what his plans caused to Riku and he truly regretted how awful he had treated Naminé and Roxas.
But there's of course also something from Nomura, lol.
-- Ansem the Wise says to Aqua “Everything is born from sleep.” What does this mean?
Nomura : In that scene the ones who are calling for “Sora” are the ones who have already disappeared from the world. But in the world of KH there is no concept of death, that for example they are just sleeping within Sora’s heart. If you can just wake them up, they’ll be able to return to the world, they would be “born from sleep”. That there would be a possibility of this, is what Ansem the Wise is saying. Even Aqua, who isn’t in the realm of light, would be born from sleep.
Bolded for better view...;P