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answers to the pairwise comparisons. There are two options for achieving
this. The first option is to convert the pairwise answers into individual
ratings using the procedure described below. Once the individual ratings
are obtained, we can use an incremental SVD algorithm to update the
model and to generate the new user vector. While the resulting model is
not a perfect SVD model, the folding-in procedure still provides a fairly
good approximation of the new user vector. The second option is to match
the newcomer's responses with existing users and to build the newcomer's
profile based on the profiles of the corresponding users. We assume that
a user will get good recommendations if like-minded users are found.
First, we map the ratings of existing users into pairwise comparisons using
Equation (16.8). Next, using the Euclidian distance, we find among existing
users those who are most similar to the newcomer. Once these users have
been identified, the profile of the newcomer is defined as the mean of their
vectors.
16.3.6
Selecting the Next Pairwise Comparison
We take the greedy approach for selecting the next pairwise comparison, i.e.
given the responses of the newcomer to the previous pairwise comparisons,
we select the next best pairwise comparison. Figure 16.4 presents the
pseudo code of the greedy algorithm. We assume that the algorithm gets
N ( v ), as an input. N ( v ) represents the set of non-newcomer similar users
that was identified based on pairwise questions answered so far by the
newcomer v .
In lines 3-15, we iterate over all candidate pairs of items. For each pair,
we calculate its score based on its weighted generalized variance. For this
purpose, we go over (lines 5-10) all possible outcomes C of the pairwise
question.Inline6,wefind N ( v, i, j, C ) which is a subset of N ( v )which
contains all users in N ( v ) that have rated items i and j with ratio C ,where
C uij is calculated as in Equation (16.8). Since in a typical recommender
system we cannot assume that all users have rated both item i and item j ,
we treat these users as a separate subset and denote it by N ( v, i, j,
).
In lines 7-9, we update the pair's scores. We search for the pairwise
comparison that best refines the set of similar users. Thus, we estimate
the dispersion of the p u vectors by first calculating the covariance matrix
(line 7). The covariance matrix Σ is a f
f matrix where f is the number of
latent factors. The covariance matrix gathers all the information about the
individual latent factor variabilities. In line 8, we calculate the determinant
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