How are the data points assigned to their locations in the geometric space? I didn't notice any mention of that. What makes something "more like" a thriller and

How are the data points assigned to their locations in the geometric space? I didn't notice any mention of that. What makes something "more like" a thriller and "less like" a comedy, for example? We can all tell the intuitive difference, but what markers serve best to precisely assign a mathematical distance? I know very little about this problem space, so these are actual questions, not at all rhetorical.