A short solution is this (PHP 5.3+):
$output['alternate_title'] = $output['alternate_title'] ?:'';
You get either the value of the variable, if it doesn't evaluate to false, or the false expression. (The one after the ':')
Using the ternary Operator, without the "if true" parameter, will return the result of the test expression (The first one ) Since undefined evaluates to false, the false expression will be returned.
In PHP 7 there is the slightly more elegant Null coalescing operator:
$output['alternate_title'] = $output['alternate_title'] ?? '';
(It would be nice with a default assignment operator like '?=')