Automatically Selectable Kaede
Though I'm not sure what triggers her appearance, if Kaede shows up in one of the random matches (that is, not five, eight or 'nine') and you defeat her, she automatically appears on the roster of selectable characters from then on. So be sure to save the game!
Play as Kaede
At the character selection screen, highlight Rain, then press down, down, left, left, up.
Play as Rai-On
At the character selection screen, highlight Byakko, then press up, down, left, left, right, left, up.
Automatically Selectable Kaede...