For the definition of SNN similarity provided by Algorithm 9.10, the cal- culation of SNN distance does not take into account the position of shared

neighbors in the two nearest neighbor lists. In other words, it might be de-

sirable to give higher similarity to two points that share the same nearest

neighbors in the same or roughly the same order.

(a) Describe how you might modify the definition of SNN similarity to give

higher similarity to points whose shared neighbors are in roughly the

same order.

(a) Describe how you might modify the definition of SNN similarity to give

higher similarity to points whose shared neighbors are in roughly the

same order.(b) Discuss the advantages and disadvantages of such a modification.

(a) This can be done by assigning weights to the points based on their
position in the nearest neighbor list. For example, we can weight the
i
th point in the nearest neighbor list by n ? i + 1. For each point, we
then take the sum or product of its rank on both lists. These values are
then summed to compute the similarity between the two objects. This
approach was suggested by Jarvis and Patrick [5].
(b) Such an approach is more complex. However, it is advantageous if it is
the case that two objects are more similar if the shared neighbors are
roughly of the same rank. Furthermore, it may also help to compensate
for arbitrariness in the choice of k.