Decision Trees and Recommender Systems - Data Mining with Decision Trees: Theory and Applications - page 268

of Σ which corresponds the generalized variance of the users' profiles. The
usefulness of GV as a measure of the overall spread of the distribution is
best explained by the geometrical fact that it measures the hypervolume
that the distribution of the random variables occupies in the space.
In conclusion, the greedy algorithm selects the next pairwise compari-
son as the pair of items minimizes the weighted generalized variance:

NextPair ≡ argmin

( i,j )

| N ( v, i, j, C ) |· GV ( N ( v, i, j, C )) . (16.9)

C

Before the first interaction of the newcomer u with the system, we
initialize the similar users set as the whole set of existing users, i.e.:
N ( v ) U . After selecting the best pair, we present the pairwise comparison

to the newcomer and wait for her response. Based on the response, we can
update the set of similar users to a corresponding subset. Specifically, if
the newcomer responded with C to the comparison between ( i, j ), then
N ( v )

←

N ( v, i, j, C ). Consequently, the process can be recursively repeated
with the new set of similar users. If the newcomer is not familiar with one
of the items, we continue the process with N ( v )

←

← N ( v, i, j, ∅ ).

Fig. 16.5 An algorithm for selecting the next pairwise comparison.