you need to get not selected options and hide()
them in subactivity. and not forget to show selected ones.
//get not selected ones
var arr1 = $('#filterActivity option:not(:selected)');
//iterate and hide
$("#filterSubActivity").children("optgroup[label='" + arr1[j].value + "']").hide();
here is demo: http://jsfiddle.net/btevfik/q62PK/