Databases Reference
In-Depth Information
In the
movie-ratings
algorithm, the prediction
r
u,t
of the general interest of a user
u
in the concept
represented in a tag
t
, that is, the tag preference, is estimated as follows:
r
u,t
=
m
∈
I
t
w
(
m, t
)
r
u,m
m∈I
t
w
(
m, t
)
∗
(4.2)
In this equation,
I
t
corresponds to the set of all items tagged with
t
. The explicit overall rating that
u
has given to movie
m
is denoted as
r
u,m
. The general idea of the method is thus to propagate the
overall rating value to the tags of a movie according to their importance.
In this work, however, we are interested in predicting the rating for a tag in the context of the target
user
u and
the target item
i
. Note that the rating prediction in Equation (4.2) does not depend on the
target item
i
at all. Our tag prediction function,
r
u,i,t
calculates a prediction for the target tag
t
,given
user
u
and item
i
, as follows:
r
u,i,t
=
m
∈
similarItems
(
i,I
t
,k
)
w
(
m, t
)
r
u,m
m∈similarItems
(
i,I
t
,k
)
w
(
m, t
)
∗
(4.3)
Instead of considering all items that received a certain tag as done in [Sen et al., 2009b], we only
consider items that are similar to the item at hand, thereby avoiding the averaging effect of “global” cal-
culations. In Equation (4.3), the calculation of neighboring items is contained in the
similarItems
(
i, I
t
,k
)
function which returns the
k
most similar items to
i
from
I
t
.
The similarity of items is measured with the adjusted cosine similarity metric. Note that we also
ran experiments using the Pearson correlation coecient as a similarity metric, which, however, led to
poorer results. As another algorithmic variant, we have tried to factor in the item similarity values as
additional weights in Equation (4.3). Again, this did not lead to further performance improvements but
rather worsened the results.
Note that when using the user's explicit overall rating
r
u,m
as in Equation (4.2), no prediction can be
made for the tag preference if user
u
did not rate any item
m
tagged with
t
, i.e., if
I
t
∩ratedItems
(
u
)=
∅
.
In our previous work [Gedikli and Jannach, 2010c], we therefore also incorporated the recursive prediction
strategy from [Zhang and Pu, 2007] into the tag preference prediction process, which lead to a slight
performance improvement. Since such an performance improvement was, however, also observed for Sen
et al.'s original methods, we will not further discuss these generally-applicable technique here in greater
depth, see [Gedikli and Jannach, 2010c] for details of the evaluation.
4.4 Predicting item ratings from tag preferences
In [Sen et al., 2009b], the best-performing tag-based recommendation algorithm with respect to
precision
is a hybrid which combines the SVM-based method
regress-tag
and the tag-agnostic matrix factoriza-
tion approach
funk-svd
[Funk, 2006]. In this work, we therefore propose to parameterize and evaluate
the
regress-tag
method using item-specific tag preferences. Note again that these tag preferences can
be explicitly available or derived as described above in Equation (4.3). In addition to that, we report
accuracy results when using item-specific tag preferences for Sen et al's
cosine-tag
method, in order to
study how this approach, which we proposed in our previous work [Gedikli and Jannach, 2010c], performs
on additional data sets.
The
regress-tag
algorithm.
The
regress-tag
method from [Sen et al., 2009b] is based on deter-
mining linear equations - one for each movie - which capture the possibly complex relationship between
the user's tag preferences for the tags of a given item and the overall item rating. The prediction function
for a user
u
and an item
i
is defined as follows, where
h
0
to
h
n
are the coecients of the linear equations
and
r
u,t
i
from Equation (4.2) corresponds to the estimated tag preferences for the tags
t
1
,..., t
n
attached
to item
i
:
(4.4)
In [Sen et al., 2009b], the coe
cients
h
0
to
h
n
were chosen with the help of regression support vector
machines and the
libsvm
library [Chang and Lin, 2011] because this led to the most accurate results when
compared with other methods for choosing the parameters such as least-squares optimization.
regress
-
tag
(
u,i
)=
h
0
+
h
1
∗
r
u,t
1
+
...
+
h
n
∗
r
u,t
n
