So, was reading through bios and what not and maybe I'm not the only one to come to this assumption but I think Noel and Anna are the children of Radomus for a few reasons.
He's very aware the importance of the amulet belonging to Anna but chooses to keep it. Radomus isn't a jerk or an idiot, he knows the importance of the amulets and let's (Protagonist) keep the other. Why not just switch so at least Anna can be happy.
During the Luna chapter he denies Luna being his real daughter but unlike Serra he doesn't deny ever having children.
Anna and Noel only know an inkling about their father and nothing about their mother and Radomus' wife is dead before the start of the story.
Radomus' involvement (just speculating) has to be more than just being a gym leader and Anna's ability to read/sense Aura (also speculation) I feel are connected.
Finally, only three humans in this game have glowing purple eyes. That was my first, main and final argument but I thought I'd give a little bit more.
I read somewhere that people think there is a crazy Serra, Radomus, El love triangle but until I know more about Lin (who I have a ton of theories on too) I think he may just be yet another sad used puppet like Corey.
P.S. Seriously only people with glowing purple eyes, don't throw curveballs at me Ame.