Normalization of Distance and Similarity in Sequence Analysis

We explore the relations between the notion of distance and a feature set-based concept of similarity and show that this concept of similarity has a spatial interpretation that is complementary to distance: it is interpreted as "direction." Furthermore, we show how proper normalization leads to distances that can be directly interpreted as dissimilarity: Closeness in normalized space implies and is implied by similarity of the same objects, while remoteness implies and is implied by dissimilarity. Finally, we show how, in research into destandardization of the life course, properly normalizing may drastically and unequivocally change our interpretation of intercohortal distances.