AFAIK, it requires a Microsoft Account. You can create one, even with non-Microsoft email addresses. I've heard people complain they don't want a Hotmail account, but I've succesfully set up a Microsoft account for my wife with her email address from our internet provider.
In the signup page, don't click 'Or get a new email address', but just enter your Yahoo Mail. This will also be your 'username' (what you use to login to your Microsoft Account):
After that, you can login to your account and link to your Twitter, Flickr, Facebook, etc accounts.