Importance of prototype-prototype similarity

When $\beta \neq 0$, the $S_p$ matrix gives us additional cues on how the prototypes are related to each other, thereby providing information on how the video segments should be clustered. In the email example, we used the word-length as cue for keyword similarity and with this cue we are able to pick up the right clustering of the emails (figure 5(f)). Furthermore, the $S_p$ also helps to alleviate the sensitivity to over-clustering of features into prototypes, by strengthening the correspondence between the segments which have similar but not necessarily identical prototypes.