Alzheimers behavior question?

I understand the restlessness, forgetfulness, and occasional irritability. But, what would make an Alzheimer's patient "hone in on" one particular person? The patient sometimes follows this one person and nitpicks at them or even just starts arguments but only if others aren't around or the patient thinks no one else can hear. This person can be just sitting quietly watching TV, not saying a word. When someone else walks in, the "patient" backs off. This happens on a daily basis. What makes them (the patient) do this?