Alias files are stored in the folder they appear in. So for example, an alias you have placed on the desktop while logged into your user account will be in ~/Desktop, the desktop folder in your user account's home folder.
However, the desktop can also display other things, like mounted external hard drives or connected servers. (You set this in Finder preferences General tab.) The screen also displays other things that are not part of the Desktop, like the Dock, so are you sure it is alais files that are missing & not something else?